# People

## Jerry Vaughan

### Professor Emeritus

**Email: **vaughanj@uncg.edu**Personal Website: **http://www.uncg.edu/~vaughanj/**Starting year at UNCG:** 1973**Ending year at UNCG:** 2019

### Education

**Degree(s): **Ph.D. in Mathematics, Duke University (1965)

### Research

**Former Students:** Katzutomo Iinuma (M.A.), Han-Ming Chen (M.A.), Dale Lee Garvin (M.A.), David Chodounsky (M.A.), Jonathan Verner (M.A.), Catherine Payne (Ph.D.)

### Selected Publications

- “A modification of Morita’s characterization of dimension,” Pacific J. Math.
**20**(l967) l89-96. - “Note on a theorem of J. Nagata,” (with B. R. Wenner) Comp. Math.
**21**(l969) 4-6. - “Linearly ordered collections and paracompactness,” Proc. American Math. Soc.
**24,**(l970) l86-192. - “Spaces of countable and point-countable type,” Trans. Amer. Math. Soc.
**151**(1970) 341-351. - “Perfect mappings and spaces of countable type,” Canad. J. Math.
**22**(1970) 1208-1210. - “Paracompactness and elastic spaces,” (with H. Tamano) Proc. Amer. Math. Soc.
**28**(l971) 299-303. - “Lexicographic products and perfectly normal spaces,” Amer. Math. Monthly
**78**(1971) 533-536. - “Linearly stratifiable spaces,” Pacific J. Math.
**43**(1972) 253-266. - “Product spaces with compactness-like properties,” Duke Math. J.
**39**(1972) 611-617. - “Some recent results in the theory of [a,b]-compactness,” TOPO 72-General Topology and its Applications. Second Pittsburgh International Conference, December l9-22, 1972. Springer-Verlag Lecture Notes in Mathematics, No. 378. pp. 534-550.
- “Products of initially m-compact spaces,” (with R. M. Stephenson, Jr.) Trans. Amer. Math. Soc.
**196**(1974) 177-189. - “A note on [a,b]-compactness,” (with R. E. Hodel) General Topology and Appl.
**4**(1974) 179-189. - “Some properties related to [a,b]-compactness,” Fund. Math.
**87**(1975) 252-260. - “Examples of ultrametrics,” Amer. Math. Monthly
**82**(1975) 749-752. - “Convergence, closed projections, and compactness,” Proc. Amer. Math. Soc.
**51**(1975) 469-476. - “Non-normal products of -metrizable spaces,” Proc. Amer. Math. Soc.
**194**(1975) 203-208. - “Total nets and filters,” Proceedings of the Memphis State University Conference. Lecture Notes in Pure and Applied Mathematics, Vol.
**24**, Marcel Dekker, Inc. New York (1976) 259-265. - “Some examples concerning -bounded spaces,” Set-Theoretic Topology, G. M. Reed, Ed. Academic Press, 1977, 359-369.
- “Products of perfectly normal sequentially compact spaces,” Journal London Math. Soc. (2)
**14**(1976) 517-520. - “Products of topological spaces,” General Topology and Appl.
**8**(1978) 207-217. -
- “Products of [a,b]-chain compact spaces,” Houston J. Math.
**3**(1977) 569-578. - “Products of [a,b]-chain compact spaces,” (Research Announcement) in “Proceedings of the Fourth Prague Symposium, 1976, Part B”. Society of Czechoslovak Mathematicians and Physicists, Prague 1977. pp. 471-476.

- “Products of [a,b]-chain compact spaces,” Houston J. Math.
- “A countably compact space and its products,” Proc. Amer. Math Soc.
**71**(1978) 133-137. - “Discrete sequences of points,” Topology Proceedings,
**3**(1978) 237-265. - “A countably compact, first countable, non-normal T2-space,” Proc. Amer. Math. Soc.
**75**(1979) 339-342. - “Some cardinals related to c and topology,” in “Proceedings: Conference on metric spaces, generalized metric spaces, and continua” (Guilford College), 1979.
- “Countably compact, locally countable T2-spaces,” Proc. Amer. Math. Soc.
**80**(1980) 147-153. - “Functions with a proper local maximum in each interval,” (with E. E. Posey), Amer. Math. Monthly
**90**(1983) 281-282. - “On first countable, countably compact spaces, I: (1, 1*)-gaps” (with Peter Nyikos). Trans. Amer. Math. Soc.,
**279**(1983) 463-469. - “Powers of spaces of non-stationary ultrafilters,” Fund. Math.,
**114**(1983) 5-14. - “Countably compact and sequentially compact spaces,” in “Handbook of Set-theoretic Topology”, Kunen and Vaughan Ed., North-Holland Publishing Co. Amsterdam, 1984.
- “Cardinalities of certain closed filters,” Topology Proc.
**8**(1983) 333-345. - “Extrema and nowhere differentiable functions,” (with E. E. Posey) Rocky Mountain Journal of Mathematics
**16**(1986) 661-668. - “Sequentially compact, Franklin-Rajagopalan spaces,” (with Peter Nyikos) Proc. Amer. Math. Soc.
**101**(1987) 149-155. - “Nowhere monotone and Cantor functions,” (with Togo Nishiura and E. E. Posey). Real Analysis Exchange
**12**(1986-87) 478-495. - “On the cardinality of prime closed filters,” in “General Topology and its Relations to Modern Analysis and Algebra VI (Proc. Sixth Prague Topological Symposium)” Z. Frolik (ed.), Heldermann Verlag, Berlin, 1986 (611-616).
- “A countably compact, first countable, nonnormal T2-space which is almost compact,” Glasnik Math.
**23**(1988) 147-152. - “The smallest number of free prime closed filters,” (with Jan Pelant and Petr Simon) Fund. Math
**131**(1988). - “Strong homology and the proper forcing axiom,” (with Alan Dow and Petr Simon) Proc. Amer. Math. Soc.
**106**(1989) 821-828. - “Some subspaces of ordinals with normal products,” (with Eric van Douwen) in “Papers on General Topology and Related Category Theory and Topological Algebra”, Volume
**552**of the Annals of the New York Academy of Sciences, (1989) 169-172. - “Small uncountable cardinals and Topology,” in
**Problems in Topology**, eds., Jan van Mill and G.M. Reed, North-Holland Pub. Co. Amsterdam (1990)195-218. - “A comparison of two constructions in topology,” Topology Proc. 15 (1990) 185-198.
- “The Scarborough-Stone problem for Hausdorff spaces,” (with Peter Nyikos) Topology and Appl.
**44**(1992) 309-316. - “Accessible and biaccessible points in contrasequential spaces,” (with Alan Dow) Annals of the New York Academy of Sciences, Vol 704 (1993) 92-102.
- “On Frolik’s characterization of class P,” Czechoslovak Mathematical Journal
**44**(1994) 1 – 6. - “Modeling expanding universes in Euclidean spaces,” (with Suzanne M. Lea and E. E. Posey) Monographs in Undergraduate Mathematics, Vol 20, Journal of Undergraduate Mathematics, Guilford College, Greensboro 1994.
- “A countably compact, separable space which is not absolutely countably compact,” Comment. Math. Univ. Carolinae 34, 1 (1995) 197-201
- “Is * acc?” (with Jan van Mill), Papers on General Topology and Applications, Annals of the New York Acad. Sci. Vol 767 (1995) 161 -164.
- “The Dugundji extension property can fail in $\omega_{\mu}$-metrizable spaces,” (with Ian S. Stares) Fundamenta Mathematicae 150 (1996) 11-16.
- “On the product of a compact space with an absolutely countably compact space,” Papers on General Topology and Applications, Annals of the New York Academy of Sciences, Vol. 788 (1996) 203-208.
- “From countable compactness to absolute countable compactness”, (with Mary Ellen Rudin and Ian Stares) Proc. Amer. Math. Soc. 25 (1997) 927-934.
- “On Dow’s reflection theorem for metrizable spaces,” Topology Proc (22 (1997) 351 -361.
- “Nearly metacompact spaces,” with Elise Grabner and Gary Grabner, Topology and Appl. 98 (1999) 191-201.
- “Almost disjoint families and property (a),” with Paul J. Szeptycki Fundamenta Mathematicae, Fund. Math. 158 (1998).
- “An introduction to reflection theorems for cardinal functions,” Proceedings Galway-Oxford Topology Conference, Topology Atlas 1998.
- “John Henderson Roberts,” Topology Proceedings, 23 (1998) 201-218.
- “Reflection theorems for cardinal functions,” (with Richard E. Hodel) Topology & Applications. 100 (2000) 47-66
- “Universal ultrametric spaces of smallest weight,” Topology Proceedings 24 (1999) 611- 619..
- “Two spaces homeomorphic to Seq(p),” Commentationes Mathematicae. Univ. Carolinae 42,1 (2001) 209-218.
- “Zero dimensional spaces from linear structures,” Indagationes Mathematicae 12 (4) (2001) 585-596
- “Universal ultrametric spaces of weight $\tau^\omega$,” Topology Proceedings 27 No. 1 (2003), pp. 345-349
- “Two step iteration of almost disjoint families,” Journal of Symbolic Logic 69 no. 1 (2004) 81-90.
- “Countable Compactness,” Encyclopedia of General Topology, K. P. Hart, J. Nagata, and J. E. Vaughan, eds, Elsevier (2004) 174-176.
- “Heredity of $\tau$-pseudocompactness,” Scientiae Mathematicae Japonicae, 62, No 2 (2005) 221-225
- “The Scarborough-Stone Problem,” Open Problems in Topology, Justin Moore and Michael Hrusak, eds. (to appear)
- “Countably compact hyperspaces and Frolik sums” with Istvan Juhasz, Topology and Appl. Volume 154, Issue 12, 15 June 2007, Pages 2434-2448 Download: the PDF file.
- “Mr\’owka maximal almost disjoint families for uncountable cardinals” with Alan Dow, Topology and Appl., Volume 157, Issue 8 (1 June 2010), 1379-1394.
- “Ordinal Remainders of $\psi$-spaces” with Alan Dow, Topology and Appl., (Special Issue in memory of Melvin Henriksen) volume 158, issue 14, (1 September 2011) pp. 1852 – 1857.
- “Ordinal Remainders of classical $\psi$-spaces” with Alan Dow, Fundamenta Mathematicae, 217 (2012) 83-93.
- “Fibers of continuous real-valued functions on $\psi$-spaces” with Catherine Payne, Topology and Appl., (Special Issue in memory of Mary Ellen Rudin, Guest Editors Gary Gruenhage and Peter Nyikos) Volume 195, November 2015, Pages 256-264
- “Companions of directed sets and the Ordering Lemma”, Topology and Appl., Special Issue in Memory of Alex Chigogidze, Guest Editor Vesko Valov, to appear
- “On the paracompactness of a class of monotonically normal spaces” with Peter Nytkos, Electronically published on September 24, 2019 , Topology Proceedings (to appear in Volume 56, in print in October 2020)

### BOOKS

**The Handbook of Set-Theoretic Topology**, editors K. Kunen and J.E. Vaughan, North-Holland Pub. Co., Amsterdam 1984, (1273 pages).

**The Encyclopedia of General Topology,** edited with J. Nagata and K. Hart, Elsevier BV 2005.

### Brief Biography

Dr. Vaughan earned a Ph.D. in 1965 from Duke University, and he joined the UNCG faculty in 1973. His research studied general topology, set theory and logic, functional analysis, and set-theoretic topology. Dr. Vaughan retired with emeritus status at the end of the spring semester in 2019 after 46 years of service.