Professor
Mathematical Sciences
Office
Marcus White Hall
111
Monday
9:00 am - 9:20 am
10:45 am - 12:05 pm
Wednesday
9:00 am - 9:20 am
10:45 am - 12:05 pm
Friday
9:00 am - 9:20 am
10:45 am - 12:05 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, Annuaire Univ. Sofia Fac. Math. Mec. 80 (1986), no. 1, 31 – 43.
PDF File - Sequentially closed and absolutely closed spaces, Boll. Un. Mat. Ital. B(7) 1 (1987), no. 3, 849 – 860.
Co-author: D. Dikranjan
PDF File - Topological spaces with no compactly determined extensions, Proceedings of the Seventeenth Spring Conference of the Union of Bulgarian Mathematicians, Sunny Beach, Bulgaria, April 6-9, (1988), 151 – 155.
PDF File - Sequentially P-closed spaces, Rend. Istit. Mat. Univ. Trieste 20 (1988), no. 1, 1 – 17.
PDF File (The original publication is available via http://rendiconti.dmi.units.it/volumi/20/01.pdf.) - On sequential properties of Noetherian topological spaces, Topology Proc. 28 (2004), No. 2, 487 – 501.
Co-author: H. Minchev
PDF File (The original publication is available via http://www.topology.auburn.edu/tp/reprints/v28/tp28210.pdf.) - Dense C-embedded subspaces of products, Sci. Math. Jpn. 64 (2006), No. 3, 509 – 515.
Co-authors: W. W. Comfort and L. Recoder-Núñez
PDF File (The original publication is available via http://www.jams.or.jp/scm/contents/e-2006-6/2006-58.pdf.) - M-embedded subspaces of certain product spaces, Topology Appl. 155 (2008), No. 17-18, 2188 – 2195.
Co-authors: W. W. Comfort and L. Recoder-Núñez
PDF File (The original publication is available via http://dx.doi.org/10.1016/j.topol.2007.04.017.) - On the continuity of factorizations, Appl. Gen. Topol. 9 (2008), No. 2, 263 – 280.
Co-authors: W. W. Comfort and L. Recoder-Núñez
PDF File (The original publication is available via https://doaj.org/article/c072a402700340278862625992d6f91e.) - Functional dependence on small sets of indices, Sci. Math. Jpn. 69 (2009), No. 3, 363 – 377.
Co-author: W. W. Comfort
PDF File (The original publication is available via http://www.jams.or.jp/scm/contents/e-2009-2/2009-18.pdf.) - Continuous mappings on subspaces of products with the κ-box topology, Topology Appl. 156 (2009), No. 16, 2600 – 2608.
Co-author: W. W. Comfort
PDF File (The original publication is available via http://dx.doi.org/10.1016/j.topol.2009.04.015.) - On two conjectures about faulty hypercubes, Graph Theory Notes N. Y. LVII (2009), 34 – 38.
Co-authors: N. Castañeda, V. Gochev, F. Latour
PDF File (The original publication is available via http://gtn.kazlow.info/GTN57.pdf.) - Path coverings with prescribed ends of the n-dimensional binary hypercube, Congr. Numer. 197 (2009), 193 – 205.
Co-authors: N. Castañeda, V. Gochev, F. Latour
PDF File - Hamiltonian laceability of hypercubes with faults of charge one, Congr. Numer. 198 (2009), 15 – 30.
Co-authors: N. Castañeda, V. Gochev, F. Latour
PDF File - On k-semi-perfect 1-factorizations of Qn and Craft's conjecture, Graph Theory Notes N. Y. LVIII (2010), 36 – 41.
Co-author: V. Gochev
PDF File (The original publication is available via http://gtn.kazlow.info/GTN58.pdf.) - On path coverings of hypercubes with one faulty vertex, Graph Theory Notes N. Y. LVIII (2010), 42 – 47.
Co-authors: N. Castañeda, V. Gochev, F. Latour
PDF File (The original publication is available via http://gtn.kazlow.info/GTN58.pdf.) - Embedded paths and cycles in faulty hypercubes, J. Comb. Optim. 20 (2010), No. 3, 224 – 248.
Co-author: N. Castañeda
PDF File (The original publication is available at Springer via http://dx.doi.org/10.1007/s10878-008-9205-6.) - Classifying simple closed curve pairs on the 2-sphere and a generalization of the Schoenflies theorem, Topology Appl. 158 (2011), No. 6, 748 – 760.
Co-authors: R. Franzosa and D. Look
PDF File (The original publication is available via doi:10.1016/j.topol.2011.01.016.) - Continuous extensions of functions defined on subsets of products, Topology Appl. 159 (2012), No. 9, 2331 – 2337.
Co-author: W. W. Comfort
PDF File (The original publication is available via doi: 10.1016/j.topol.2011.08.030.) - Continuous extensions of functions defined on subsets of products with the κ-box topology, Topology Proc. 42 (2013), 209 – 219.
Co-authors: W. W. Comfort and D. Rivers
PDF File (The original publication is available via http://www.topology.auburn.edu/tp/reprints/v42/tp42017.pdf.) - The non-Hausdorff number of a topological space, Topology Proc. 44 (2014), 249 – 256.
PDF File (The original publication is available via http://www.topology.auburn.edu/tp/restricted/v44/tp44022.pdf.) - Path coverings with prescribed ends in faulty hypercubes, Graphs and Combinatorics 31 (2015), 833 – 869.
Co-author: N. Castañeda
PDF File (The original publication is available at Springer via http://link.springer.com/article/10.1007/s00373-014-1426-0.) - Regular Gδ-diagonals and some upper bounds for cardinality of topological spaces, Acta Mathematica Hungarica 149 (2016), No. 2, 324 – 337.
Co-authors: M. Tkachenko and V. Tkachuk
(The original publication is available at Springer via http://link.springer.com/article/10.1007/s10474-016-0614-1.) - Cardinal invariants for κ-box products: weight, density character and Souslin number, Dissertationes Mathematicae 516 (2016), 1 – 41.
Co-author: W. W. Comfort
(The original publication is available via https://www.impan.pl/en/publishing-house/journals-and-series/dissertationes-mathematicae/all/516.) - The non-Urysohn number of a topological space, Houston J. Math. 43 (2017), No. 1, 223 – 235.
(The original publication is available via https://www.math.uh.edu/~hjm/Vol43-1.html.) - Generalizations of two cardinal inequalities of Hajnal and Juhász, Topology Appl. 221 (2017), 425 – 431.
(The original publication is available via doi: 10.1016/j.topol.2017.02.026.) - Proof of Locke's conjecture, I, Palestine Journal of Mathematics 6 (2017), No. 2, 345 – 371.
Co-author: N. Castañeda
(The original publication is available via http://pjm.ppu.edu/sites/default/files/papers/PJM_April_2017_0.pdf.) - Cardinal inequalities for Urysohn spaces involving variations of the almost Lindelöf degree, Serdica Math. J. 44 (2018), 195 – 212.
(The original publication is available via http://www.math.bas.bg/serdica/2018/2018-195-212.pdf.) - More on the cardinality of S(n)-spaces, Serdica Math. J. 44 (2018), 227 – 242.
Co-author: L. Kočinac
(The original publication is available via http://www.math.bas.bg/serdica/2018/2018-227-242.pdf.) - Cardinalities of weakly Lindelöf spaces with regular G_κ-diagonals, Topology Appl. 259 (2019), 80 – 89.
(The original publication is available via doi: 10.1016/j.topol.2019.02.023.) - Cardinal inequalities for S(n)-spaces, Acta Mathematica Hungarica 159 (2019), No. 1, 229 – 245.
(The original publication is available at Springer via http://link.springer.com/article/10.1007/s10474-019-00939-0.) - Cardinal inequalities with Shanin number and π-character, Bull. Belgian Math. Soc. Simon Stevin, 29 (2022), no. 3, 389 – 403.
Co-author: V. Tkachuk
(The original publication is available at Project Euclid via doi: 10.36045/j.bbms.220321a.) - More on cardinality bounds involving the weak Lindelöf degree, Quaestiones Mathematicae 46 (2023), no. 4, 745 – 760.
Co-authors: A. Bella and N. Carlson
(The original publication is available via https://www.tandfonline.com/doi/abs/10.2989/16073606.2022.2040634.) - On the upper bound of the cardinality of Hausdorff topological spaces, Topology Appl., 338 (2023), Article 108651.
(The original publication is available via https://doi.org/10.1016/j.topol.2023.108651.) - On spaces with a π-base with elements with compact closure, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM 118 (2024), no. 1, article 26. Published online on November 11, 2023.
Co-authors: A. Bella and N. Carlson
(The original publication is available via https://doi.org/10.1007/s13398-023-01526-3.)
- Superneighborhood spaces and extensions of topological spaces, Annuaire Univ. Sofia Fac. Math. Mec. 80 (1986), no. 1, 31 – 43.
- Work in Progress
- On the De Groot's inequality (preprint).
- Proof of Locke's conjecture, II (preprint).
Co-authors: N. Castañeda, V. Gochev, F. Latour - On the infinitude of prime divisors of the range of a non-constant polynomial (preprint).
Memberships & Affiliations
American Mathematical Society (AMS)
Mathematical Association of America (MAA)
Courses Taught
Spring 2024
MWF 9:25 pm - 10:35 pm - MATH 152 - Calculus I (section 03), EDB 109
MWF 12:15 pm - 1:25 pm - MATH 152 - Calculus I (section 04), EDB 105
MW 1:40 pm - 2:50 pm - MATH 152 - Calculus I (section 01), EDB 105
Office Hours Spring 2024
MWF 9:00 am - 9:20 am in MW 111
MWF 10:45 am - 12:05 pm in MW 111
or by appointment