
Professor
Mathematical Sciences
Office
Marcus White Hall
111
Monday
8:50 am - 9:20 am
1:30 pm - 2:40 pm
Wednesday
8:50 am - 9:20 am
1:30 pm - 2:40 pm
Friday
8:50 am - 9:20 am
1:30 pm - 2:40 pm
Or by appointment
Education
Areas of Expertise
- General, Categorical, and Geometric Topology and their Applications
Product spaces; continuous extensions of functions defined on subspaces of product spaces; cardinal invariants; covering properties; compact, pseudocompact, countable compact and sequentially compact spaces; closure operators; P-minimal and P-closed spaces; sequential convergence; sequential spaces; extensions of topological spaces; supertopological spaces; neighborhood spaces; separation axioms; proximities; Noetherian spaces; applications of topology in number theory and geographic information systems. - Graph Theory
Hamiltonian graphs
Publications, Research & Presentations
-
Publications in peer-reviewed journals
- Superneighborhood spaces and extensions of topological spaces, 80 (1986), no. 1, 31 鈥 43.
- Sequentially closed and absolutely closed spaces, Boll. Un. Mat. Ital. B(7) 1 (1987), no. 3, 849 鈥 860.
Co-author: D. Dikranjan - Topological spaces with no compactly determined extensions, , Sunny Beach, Bulgaria, April 6-9, (1988), 151 鈥 155.
- Sequentially P-closed spaces, 20 (1988), no. 1, 1 鈥 17.
(The original publication is available via .) - On sequential properties of Noetherian topological spaces, Topology Proc. 28 (2004), No. 2, 487 鈥 501.
Co-author: H. Minchev
(The original publication is available via http://www.topology.auburn.edu/tp/reprints/v28/tp28210.pdf.) - Dense C-embedded subspaces of products, 64 (2006), No. 3, 509 鈥 515.
Co-authors: W. W. Comfort and L. Recoder-N煤帽ez
(The original publication is available via .) - M-embedded subspaces of certain product spaces, Topology Appl. 155 (2008), No. 17-18, 2188 鈥 2195.
Co-authors: W. W. Comfort and L. Recoder-N煤帽ez
(The original publication is available via .) - On the continuity of factorizations, 9 (2008), No. 2, 263 鈥 280.
Co-authors: W. W. Comfort and L. Recoder-N煤帽ez
(The original publication is available via .) - Functional dependence on small sets of indices, 69 (2009), No. 3, 363 鈥 377.
Co-author: W. W. Comfort
(The original publication is available via .) - Continuous mappings on subspaces of products with the 魏-box topology, Topology Appl. 156 (2009), No. 16, 2600 鈥 2608.
Co-author: W. W. Comfort
(The original publication is available via .) - On two conjectures about faulty hypercubes, LVII (2009), 34 鈥 38.
Co-authors: N. Casta帽eda, , F. Latour - Path coverings with prescribed ends of the n-dimensional binary hypercube, Congr. Numer. 197 (2009), 193 鈥 205.
Co-authors: N. Casta帽eda, , F. Latour - Hamiltonian laceability of hypercubes with faults of charge one, Congr. Numer. 198 (2009), 15 鈥 30.
Co-authors: N. Casta帽eda, , F. Latour - On k-semi-perfect 1-factorizations of Qn and Craft's conjecture, LVIII (2010), 36 鈥 41.
Co-author: - On path coverings of hypercubes with one faulty vertex, LVIII (2010), 42 鈥 47.
Co-authors: N. Casta帽eda, , F. Latour - Embedded paths and cycles in faulty hypercubes, 20 (2010), No. 3, 224 鈥 248.
Co-author: N. Casta帽eda
(The original publication is available at Springer via .) - Classifying simple closed curve pairs on the 2-sphere and a generalization of the Schoenflies theorem, Topology Appl. 158 (2011), No. 6, 748 鈥 760.
Co-authors: R. Franzosa and
(The original publication is available via .) - Continuous extensions of functions defined on subsets of products, Topology Appl. 159 (2012), No. 9, 2331 鈥 2337.
Co-author: W. W. Comfort
(The original publication is available via .) - Continuous extensions of functions defined on subsets of products with the 魏-box topology, 42 (2013), 209 鈥 219.
Co-authors: W. W. Comfort and D. Rivers
(The original publication is available via http://www.topology.auburn.edu/tp/reprints/v42/tp42017.pdf.) - The non-Hausdorff number of a topological space, 44 (2014), 249 鈥 256.
(The original publication is available via http://www.topology.auburn.edu/tp/restricted/v44/tp44022.pdf.) - Path coverings with prescribed ends in faulty hypercubes, 31 (2015), 833 鈥 869.
Co-author: N. Casta帽eda
(The original publication is available at Springer via .) - Regular G未-diagonals and some upper bounds for cardinality of topological spaces, 149 (2016), No. 2, 324 鈥 337.
Co-authors: M. Tkachenko and V. Tkachuk
(The original publication is available at Springer via .) - Cardinal invariants for 魏-box products: weight, density character and Souslin number, 516 (2016), 1 鈥 41.
Co-author: W. W. Comfort
(The original publication is available via .) - The non-Urysohn number of a topological space, 43 (2017), No. 1, 223 鈥 235.
(The original publication is available via .) - Generalizations of two cardinal inequalities of Hajnal and Juh谩sz, 221 (2017), 425 鈥 431.
(The original publication is available via .) - Proof of Locke's conjecture, I, 6 (2017), No. 2, 345 鈥 371.
Co-author: N. Casta帽eda
(The original publication is available via .) - Cardinal inequalities for Urysohn spaces involving variations of the almost Lindel枚f degree, 44 (2018), 195 鈥 212.
(The original publication is available via .) - More on the cardinality of S(n)-spaces, 44 (2018), 227 鈥 242.
Co-author: L. Ko膷inac
(The original publication is available via .) - Cardinalities of weakly Lindel枚f spaces with regular G_魏-diagonals, 259 (2019), 80 鈥 89.
(The original publication is available via .) - Cardinal inequalities for S(n)-spaces, 159 (2019), No. 1, 229 鈥 245.
(The original publication is available at Springer via .) - Cardinal inequalities with Shanin number and 蟺-character, 29 (2022), no. 3, 389 鈥 403.
Co-author: V. Tkachuk
(The original publication is available at Project Euclid via .) - More on cardinality bounds involving the weak Lindel枚f degree, 46 (2023), no. 4, 745 鈥 760.
Co-authors: and
(The original publication is available via .) - On the upper bound of the cardinality of Hausdorff topological spaces, , 338 (2023), Article 108651.
(The original publication is available via .) - On spaces with a 蟺-base with elements with compact closure, 118 (2024), no. 1, article 26.
Co-authors: and
(The original publication is available via .)
Submitted or Accepted for Publication
- Strengthening of de Groot鈥檚 and Spadaro鈥檚 inequalities for Urysohn spaces (submitted for publication).
Work in Progress
- Proof of Locke's conjecture, II (preprint).
Co-authors: N. Casta帽eda, , F. Latour - On the infinitude of prime divisors of the range of a non-constant polynomial (preprint).
- Superneighborhood spaces and extensions of topological spaces, 80 (1986), no. 1, 31 鈥 43.
Memberships & Affiliations
American Mathematical Society (AMS)
Mathematical Association of America (MAA)
Courses Taught
Spring 2025
MWF 9:25 am - 10:35 am - , EDB 111
MWF 10:50 am - 12:00 pm - , EDB 111
MWF 12:15 pm - 1:25 pm - , EDB 111
for Calculus I (section 03)
for Calculus I (section 03)
for Calculus I (section 03)
for Calculus I (section 03)
for Calculus II (sections 04 and 06)
for Calculus II (sections 04 and 06)
for Calculus II (sections 04 and 06)
for Calculus II (sections 04 and 06)
Office Hours Spring 2025
MWF 8:50 am - 9:20 am in MW 111
MWF 1:30 pm - 2:40 pm in MW 111
or by appointment