## David J. Lutzer

## Mathematics Department

## College of William and Mary

November 8, 2012

## Education:

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

## Position:

## Research Interests:

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

## Recent Publications:

"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.

Other research papers.