David J. Lutzer

Mathematics Department

College of William and Mary


November 8, 2012

Education:

Position:

Research Interests:

Recent Publications:

  • "The Gruenhage property, property *, fragmentability, and sigma-isolated networks in generalized ordered spaces" (with H. Bennett), submitted. 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.

  • Other research papers.