David J. Lutzer

Mathematics Department

College of William and Mary

June 23, 2023

Education:

B.S., Creighton University (1964)
Diploma in Advanced Mathematics, Oxford University (1966)
Ph.D., University of Washington (1970)

Position:

Visiting Professor, University of Illinois (2017-2020)
Chancellor Professor of Mathematics, Emeritus, William and Mary
Department of Mathematics,
College of William and Mary.

Lutzer's CV

Research Interests:

General and set theoretic topology, ordered spaces, function spaces, domain representability of topological spaces, domain theory.

Undergraduate Honors Students

Cynthia Bowers, 1999, "Linear Orderings: A Sampler"

Will Funk, 2002, "Branch Spaces and Lexicographic Orderings of Trees"

Kevin Duke, 2006, "Domain Theory: Modeling Generalized Ordered Modifications of the Real Line"

Jacob Hill, 2009, "The Set of All Countable Ordinals: An Inquiry into its Construction, Properties, and a Proof Concerning Hereditary Subcompactness."

Recent Publications:

"A note on eta_1 spaces" (with H. Bennett and S. Davis), Topology Proceedings, 59(2022),25-50 . pdf version

"Topology inside omega_1" (with H. Bennett), Rocky Mountain Journal of Mathematics, 50(2020),1989-2000. pdf version

"Perfect images of generalized ordered spaces" (with G. Gruenhage), Fundamenta Mathematicae 240(2018), 175-198. pdf version

"Images of the countable ordinals" (with H. Bennett and S. Davis), Topology and its Applications, 221(2017), 610-623. pdf version

"Semi-stratifiable spaces with monotonically normal compactifications" (with H. Bennett), Topology and its Applications, 197(2016), 21-27. pdf version

"Mary Ellen Rudin and monotone normality" (with H. Bennett), Topology and its Applications, 195(2015), 50-62. pdf version

"The Gruenhage property, property *, fragmentability, and sigma-isolated networks in generalized ordered spaces" (with H. Bennett), Fundamenta Mathematicae, 223(2013), 273-294. pdf version

"A shorter proof of a theorem on hereditarily orderable spaces" (with H. Bennett), Topology Proceedings, 40(2012), 311-318. pdf version

"Choban operators in generalized ordered spaces" (with H. Bennett and D. Burke), Topology and its Applications, 160(2013), 633-647. pdf version

"Some Questions of Arhangel'skii on Rotoids" (with H. Bennett and D. Burke), Fundamenta Mathematicae, 216(2012),147-161. pdf version

"The Big Bush Machine" (with H. Bennett and D. Burke), Topology and its Applications, 159(2012), 1514-1528. pdf version

"Measurements and G-delta subsets of domains", (with H. Bennett), Canadian Mathematical Bulletin, 54(2011), 193-206. pdf version

"A note on monotonically metacompact spaces" (with H. Bennett and K.P. Hart), Topology and its Applications, 157(2010), 456-465. pdf version

"Strong completeness properties in topology" (with H. Bennett), Questions and Answers in General Topology, 27(2009), 107-124. pdf version

"Domain-Representable Spaces and Completeness", (with H. Bennett), Topology Proceedings, 34(2009), 223-244. pdf version

"Subcompactness and Domain Representability in GO-spaces on Real Numbers" (with H. Bennett), Topology and its Applications, 156(2009), 939-950. pdf version

"CBMS2005: Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States" (with S. Rodi, E. Kirkman, and J. Maxwell), American Mathematical Society, Providence RI, 2007, 354 pp. pdf version

"Domain representability of Cp(X)" (with H. Bennett), Fundamenta Mathematicae, 200(2008), 185-199. pdf version

"Domain representability of certain function spaces" (with H. Bennett), Topology and its Appl.,156 (2009), 1937-1942. pdf version

"Scott representability of some spaces of Tall and Miskin" (with H. Bennett), Applied General Topology, 9(2008), 281-292. pdf version

"Selected ordered space problems'' (with H. Bennett), pp. 3-9 in "Open Problems in Topology, II," ed. by E. Pearl, Elsevier, New York,2007. pdf version

"Amsterdam properties of Cp(X) imply discreteness of X" (with J. van Mill and V. Tkachuk), Canadian Math. Bulletin, 51(2008), 570-578. pdf version

"Scott-domain representability of a class of generalized ordered spaces" (with K.W. Duke), Topology Proceedings, 32(2008), 1-14. pdf version

"Domain-representability and the Choquet game in Moore and BCO spaces" (with H. Bennett and G.M. Reed), Topology and its Applications, 155(2008), 445-458. pdf version

"A countably-based domain representation of a non-regular Hausdorff space" (with H. Bennett), Topology Proceedings, 30(2006), 83-93. pdf version

"Domain-representability of certain complete spaces" (with H. Bennett), Houston Journal of Mathematics, 34(2008), 753-772. pdf version

"Compact G-delta sets" (with H. Bennett and R. Byerly), Topology and its Applications, 153(2006), 2169-2181. pdf version

"The NSF Budget: Not Far Away From Us", FOCUS 25(2005), 32.

"Domain-representable spaces" (with H. Bennett), Fundamenta Math., 189(2006), 255-268. pdf version

"On a question of Maarten Maurice" (with H. Bennett), Topology and its Applications, 153(2006), 1631-1638. pdf version

"Science Policy at the MAA," FOCUS 24(2004), 10-11. pdf version

"Quarter-stratifiability in ordered spaces" (with H. Bennett), Proc. Amer. Math.Soc., 134(2006), 1835-1847. pdf version

"The beta-space property in generalized ordered and monotonically normal spaces" (with H. Bennett), Topology and its Applications, 153(2006), 2218-2228. pdf version

"The arithmetic of algebraic numbers: an elementary approach" (with C-K Li), College Mathematics Journal, 35(2004), 307-309. pdf version

"Lexicographically ordered trees" (with Will Funk), Topology and its Applications, 151(2005), 275-300. pdf version

"The monotone Lindelof property and separability in ordered spaces" (with H. Bennett and M. Matveev), Topology and its Applications, 151(2005), 180-186. pdf version

"Branch space representations of lines" (with Will Funk), Topology and its Applications, 151(2005), 187-214. pdf version

"Staffing Shifts in Mathematical Sciences Departments, 1990-2000," (with J. Maxwell), Notices American Mathematical Society, 50(2003), 683-686. pdf version

"Mathematics Majors 2002," Notices American Mathematical Society, 50(2003), 235-237. pdf version

CBMS2000: Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States, (with J. Maxwell and S. Rodi), American Mathematical Society, Providence, RI, 2002, 303 pages. pdf version

"Spaces with $< \omega$-weakly uniform bases," with H. Bennett, Topology Proceedings, 27(2003). pdf version

"Metrically fibered generalized ordered spaces," with H. Bennett, Topology and its Applications, 130(2003), 283-290. pdf version

"Lines, trees, and branch spaces," with H. Bennett and M.E. Rudin, ORDER, 19(2002), 367-384. pdf version

"Linearly ordered and generalized ordered spaces," with H. Bennett, pp. 326-330 in Encyclopedia of General Topology, ed. by K.P. Hart, J. Nagata, and J. Vaughan, Elsevier, Amsterdam, 2004. pdf version

"Continuous separating families in ordered spaces and strong base conditions," with H. Bennett, Topology and its Applications 119(2002), 305-314. pdf version

"Recent developments in the topology of ordered spaces," with H. Bennett, Recent Progress in General Topology II, ed. by M. Husek and J. van Mill, Elsevier, Amsterdam, 2002, pp. 83-110. pdf version

"Advising," in Encyclopedia of Mathematics Education, ed. by L. Grinstein and S. Lipsey, pp. 14-16, RutledgeFalmer, New York, 2001.

"Cleavability in ordered spaces," with H. Bennett and R. Byerly, ORDER, 18(2001), 1-17. pdf version

"A decade of REU at William and Mary," with C. Johnson, Proceedings of the Conference on Summer Undergraduate Mathematics Research Programs, ed. by J. Gallian, American Mathematical Society, Providence, 2000, pp. 19-29. pdf version

"OIF spaces," with Z. Balogh, H. Bennett, D. Burke, G. Gruenhage, and J. Mashburn, Questions and Answers in General Topology, 18(2000), 129-141. pdf version

"Generalized ordered spaces with $\sigma$-closed discrete dense subsets," with H. Bennett and R. Heath, Proc. Amer. Math. Soc., 129 (2000), 931-939. pdf version

"Baire and Volterra spaces," with Gary Gruenhage, Proc. Amer. Math. Soc., 128 (2000), 3115-3124. pdf version

"Weakly perfect generalized ordered spaces," with H. Bennett and M. Hosobuchi, Houston J. Math., 26(2000), 609-627. pdf version

"A note on perfect ordered spaces," with H. Bennett and M. Hosobuchi, Rocky Mountain Journal of Mathematics, 29(1999), 1195-1207. pdf version

"Isomorphic Subgroups and an application of Q-linearity," with S. Fallat, C-K Li, and D. Stanford, Mathematics Magazine, 72 (1999), 388-391. pdf version

"On dense subspaces of generalized ordered spaces," with H. Bennett and S. Purisch, Topology and its Applications 93 (1999), 191-205. pdf version

"Ordered spaces with special bases," with H. Bennett, Fundamenta Math. 158 (1998), 289-299. pdf version

"A metric space of A.H. Stone and an example concerning $\sigma$-minimal bases," with H. Bennett, Proc. Amer. Math. Soc. 126 (1998), 2183-2189. pdf version

"Off-diagonal metrization theorems," with H. Bennett, Topology Proceedings 22 (1997), 37-58. pdf version

"A note on paracompactness in generalized ordered spaces," with E. van Douwen, Proc. Amer. Math. Soc. 125 (1997), 1237-1245. pdf version

"Diagonal conditions in ordered spaces," with H. R. Bennett, Fund. Math. 153 (1997), 99-123. pdf version

"Point-countability in generalized ordered spaces," with H.R. Bennett, Topology and its Applications, 71 (1996), 149-165. pdf version

"A note on Property III in generalized ordered spaces," with H.R. Bennett, Topology Proceedings 21 (1996), 15-24. pdf version

"Advising undergraduates about graduate school in mathematics: methods that work," with D. Herrmann, FOCUS, June 1995.

Papers before 1994 with MR numbers

[1] 88k:54050 Burke, D. K. ; Lutzer, D. J. On powers of certain lines. Topology Appl. 26 (1987), no. 3, 251--261).

[2] 87e:54046 Lutzer, D. ; van Mill, J. ; Pol, R. Descriptive complexity of function spaces. Trans. Amer. Math. Soc. 291 (1985), no. 1, 121--128.

[3] 87a:54039 Burke, D. ; Lutzer, D. ; Levi, S. Functional characterizations of certain $p$-spaces. Topology Appl. 20 (1985), no. 2, 161--165.

[4] 87a:54018 Dijkstra, J. ; Grilliot, T. ; Lutzer, D. ; van Mill, J. Function spaces of low Borel complexity. Proc. Amer. Math. Soc. 94 (1985), no. 4, 703--710.

[5] 85h:54058 Lutzer, D. J. Twenty questions on ordered spaces. Topology and order structures, Part 2 (Amsterdam, 1981), 1--18, Math. Centre Tracts, 169, Math. Centrum, Amsterdam, 1983.

[6] 85h:54053 Bennet, H. ; Lutzer, D. J. A note on perfect normality in generalized ordered spaces. Topology and order structures, Part 2 (Amsterdam, 1981), 19--22, Math. Centre Tracts, 169, Math. Centrum, Amsterdam, 1983.

[7] 85g:54001 Topology and order structures. Part 2. Papers presented at the second workshop on topology and linear orderings held in Amsterdam, August 1981. Edited by H. R. Bennett and D. J. Lutzer. Mathematical Centre Tracts, 169. Mathematisch Centrum, Amsterdam, 1983. iii+107 pp. ISBN: 90-6196-266-8 54-06.

[8] 85d:54041 Bennett, H. R. ; Lutzer, D. J. Generalized ordered spaces with capacities. Pacific J. Math. 112 (1984), no. 1, 11--19.

[9] 83c:54044 Kulpa, W. ; Lutzer, D. New proofs of a metrization theorem for ordered spaces. Topology and order structures, Part 1 (Lubbock, Tex., 1980), pp. 141--146, Math. Centre Tracts, 142, Math. Centrum, Amsterdam, 1981.

[10] 83b:54040 Bennett, H. R. ; Lutzer, D. J. A note on perfect ordered spaces. The Proceedings of the 1980 Topology Conference (Univ. Alabama, Birmingham, Ala., 1980). Topology Proc. 5 (1980), 27--32 (1981).

[11] 82m:54029 Lutzer, David J. A metrization theorem for generalized ordered spaces. The Proceedings of the 1979 Topology Conference (Ohio Univ., Athens, Ohio, 1979). Topology Proc. 4 (1979), no. 1, 265--269 (1980).

[12] 82k:54019 Lutzer, D. J. ; McCoy, R. A. Category in function spaces. I. Pacific J. Math. 90 (1980), no. 1, 145--168.

[13] 82k:54010 Bennett, H. R. ; Fleissner, W. G. ; Lutzer, D. J. Ultraparacompactness in certain Pixley\mhy Roy hyperspaces. Fund. Math. 111 (1981), no. 1, 11--18.

[14] 82k:54009 Bennett, H. R. ; Fleissner, W. G. ; Lutzer, D. J. Metrizability of certain Pixley\mhy Roy spaces. Fund. Math. 110 (1980), no. 1, 51--61.

[15] 82j:54063 Bennett, H. R. ; Lutzer, D. J. Certain hereditary properties and metrizability in generalized ordered spaces. Fund. Math. 107 (1980), no. 1, 71--84.

[16] 82h:54001 Topology and order structures. Part 1. Papers presented at a Workshop on Topology and Linear Orderings held at Texas Tech University, Lubbock, Tex., August 1980. Edited by H. R. Bennett and D. J. Lutzer. Mathematical Centre Tracts, 142. Mathematisch Centrum, Amsterdam, 1981. iii+184 pp. ISBN: 90-6196-228-5 54-06

[17] 82f:54046 Bennett, H. R. ; Lutzer, D. J. ; van Wouwe, J. M. Linearly ordered Eberlein compact spaces. Topology Appl. 12 (1981), no. 1, 11--18.

[18] 81d:54026 Lutzer, David J. Ordered topological spaces. Surveys in general topology, pp. 247--295, Academic Press, New York-London-Toronto, Ont., 1980.

[19] 81b:54008 van Douwen, E. K. ; Lutzer, D. J. ; Pelant, J. ; Reed, G. M. On unions of metrizable subspaces. Canad. J. Math. 32 (1980), no. 1, 76--85.

[20] 80m:54012 Lutzer, David J. Pixley-Roy topology. Proceedings of the 1978 Topology Conference (Univ. Oklahoma, Norman, Okla., 1978), I. Topology Proc. 3 (1978), no. 1, 139--158 (1979).

[21] 80j:54027 Bennett, H. R. ; Lutzer, D. J. Ordered spaces with $\sigma $-minimal bases. Proceedings of the 1977 Topology Conference (Louisiana State Univ., Baton Rouge, La., 1977), II. Topology Proc. 2 (1977), no. 2, 371--382 (1978).

[22] 80h:54038 van Douwen, Eric K. ; Lutzer, David J. On the classification of stationary sets. Michigan Math. J. 26 (1979), no. 1, 47--64.

[23] 80d:54014 Lutzer, David J. ; Przymusi\'nski, Teodor C. Continuous extenders in normal and collectionwise normal spaces. Fund. Math. 102 (1979), no. 3, 165--171.

[24] 56 16577 van Douwen, E. K. ; Lutzer, D. J. ; Przymusi\'nski, T. C. Some extensions of the Tietze-Urysohn theorem. Amer. Math. Monthly 84 (1977), no. 6, 435--441.

[25] 55 11197 Lutzer, David J. A selection-theoretic approach to certain extension theorems. Set-theoretic topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975--1976), pp. 269--275. Academic Press, New York, 1977.

[26] 55 1318 Burke, Dennis K. ; Lutzer, David J. Recent advances in the theory of generalized metric spaces. Topology (Proc. Ninth Annual Spring Topology Conf., Memphis State Univ., Memphis, Tenn., 1975), pp. 1--70. Lecture Notes in Pure and Appl. Math., Vol. 24, Dekker, New York, 1976.

[27] 55 1303 Engelking, R. ; Lutzer, D. Paracompactness in ordered spaces. Fund. Math. 94 (1977), no. 1, 49--58.

[28] 54 13844 Franklin, S. P. ; Lutzer, D. J. ; Thomas, B. V. S. On subcategories of TOP. Trans. Amer. Math. Soc. 225 (1977), 267--278.

[29] 54 6088 Aarts, J. M. ; Lutzer, D. J. On constructing bases in certain complete spaces. Nederl. Akad. Wetensch. Proc. Ser. A {\bf 79}=Indag. Math. 38 (1976), no. 3, 185--188.

[30] 53 3237 Lutzer, D. J. Some constructions in abstract measure theory. Canad. J. Math. 27 (1975), no. 4, 860--866.

[31] 52 1642 Aarts, J. M. ; Lutzer, D. J. Completeness properties designed for recognizing Baire spaces. Dissertationes Math. (Rozprawy Mat.) 116 (1974), 48 pp.

[32] 51 11424 Heath, R. W. ; Lutzer, D. J. The Dugundji extension theorem and collectionwise normality. Bull. Acad. Polon. Sci Sér. Sci. Math. Astronom. Phys. 22 (1974), 827--830.

[33] 51 9030 Heath, R. W. ; Lutzer, D. J. ; Zenor, P. L. Monotonically normal spaces. Trans. Amer. Math. Soc. 178 (1973), 481--493.

[34] 51 6746 Burke, D. ; Engelking, R. ; Lutzer, D. Hereditarily closure-preserving collections and metrization. Proc. Amer. Math. Soc. 51 (1975), 483--488.

[35] 51 6704 Heath, R. W. ; Lutzer, D. J. Dugundji extension theorems for linearly ordered spaces. Pacific J. Math. 55 (1974), 419--425.

[36] 50 14692 Lutzer, D. J. Ordinals and paracompactness in ordered spaces. TOPO 72---general topology and its applications (Proc. Second Pittsburgh Internat. Conf., Pittsburgh, Pa., 1972; dedicated to the memory of Johannes H. de Groot), pp.258--266, Lecture Notes in Math., Vol. 378, Springer, Berlin, 1974.

[37] 50 14681 Borges, C. R. ; Lutzer, D. J. Characterizations and mappings of $M\sb{i}$ spaces. Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973), pp. 34--40. Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974.

[38] 50 11134 Heath, R. W. ; Lutzer, D. J. ; Zenor, P. L. On continuous extenders. Studies in topology (Proc. Conf., Univ. North Carolina, Charlotte, N.C., 1974; dedicated to Math. Sect. Polish Acad. Sci.), pp. 203--213. Academic Press, New York, 1975.

[39] 50 8460 Lutzer, D. J. On quasi-uniform bases. Proceedings of the University of Oklahoma Topology Conference dedicated to Robert Lee Moore (Norman, Okla., 1972), pp. 104--117. Univ. of Oklahoma, Norman, Okla., 1972.

[40] 49 9797 Lutzer, D. ; Martin, H. A note on the Dugundji extension theorem. Proc. Amer. Math. Soc. 45 (1974), 137--139.

[41] 48 5009 Aarts, J. M. ; Lutzer, D. J. Pseudo-completeness and the product of Baire spaces. Pacific J. Math. 48 (1973), 1--10.

[42] 48 3018 Lutzer, D. J. On generalized ordered spaces. Dissertationes Math. Rozprawy Mat. 89 (1971), 32 pp.

[43] 46 8167 Aarts, J. M. ; Lutzer, D. J. The product of totally nonmeagre spaces. Proc. Amer. Math. Soc. 38 (1973), 198--200.

[44] 46 6292 Lutzer, David J. Another property of the Sorgenfrey line. Compositio Math. 24 (1972), 359--363.

[45] 46 853 Bennett, H. R. ; Lutzer, D. J. A note on weak $\theta $-refinability. General Topology and Appl. 2 (1972), 49--54.

[46] 45 5952 Lutzer, D. J. Semimetrizable and stratifiable spaces. General Topology and Appl. 1 (1971), no. 1, 43--48.

[47] 42#1075 Lutzer, David J. On generalized ordered spaces. 1970 Proc. Washington State Univ. Conf. on General Topology (Pullman, Wash., 1970) pp. 102--110 Pi Mu Epsilon, Dept. of Math., Washington State Univ., Pullman, Wash.

[48] 40#2013 Lutzer, D. J. ; Bennett, H. R. Separability, the countable chain condition and the Lindelof property in linearly orderable spaces. Proc. Amer. Math. Soc. 23 1969 664--667.

[49] 40#2012 Lutzer, David J. A metrization theorem for linearly orderable spaces. Proc. Amer. Math. Soc. 22 1969 557--558.

[50] 078 649 Bennett, H. R. ; Lutzer, D. J. Problems in perfect ordered spaces. Open problems in topology, 231--236, North-Holland, Amsterdam, 1990.

[51] 776 568 Bennett, H. R. ; Lutzer, D. J. Metrization, quasi-developments and $\sigma$-minimal bases. Questions Answers Gen. Topology 2 (1984), no. 2, 73--76.