Positions
Education
Areas of Specialization:
General and Geometric Topology
Research Interests:
General and Geometric Topology (dimension theory, asymptotic topology, infinite-dimensional topology, continuous selections), Continuum Theory, Functional Analysis (algebraic properties of spaces of functions, ranks of C*-algebras)
Current & Future Research:
Homogeneous spaces, infinite-dimensional spaces, topological data analysis (NSERC funded)
Publications
Simple polynomial equations over (m×m)-matrices (with V. Chatyrko), preprint.
Vietoris thickenings and complexes are homotopy equivalent, (with H. Adams and Z. Virk), submitted.
Analyzing Short Texts using Wordscores (with D. Paczay), submitted
Simple polynomial equations over (2×2)-matrices (with V. Chatyrko), Appl. Gen. Topol. 27, no. 1 (2026), 24202.
On structural numbers of topological spaces, (with V. Chatyrko), Mathematica Slovaca 5, no. 5 (2025), 1241-1248.
On discrete homogeneity (with V. Chatyrko), General topology and related fields, RIMS Kyoto University, 2024, 14-21.
Strongly locally homogeneous generalized continua of finite cohomological dimension (with P.Krupski, V. Valov, and V. Todorov), Topology Appl., 348 (2024).
On (Theta-)discrete homogeneous spaces, (with V. Chatyrko), Mathematica Slovaca, 73, no. 6 (2023), 1587-1596.
Discrete homogeneity and ends of manifolds, (with V. Chatyrko), Topology Appl. 336 (2023).
On homogeneity of Ntau, (with E. Shchepin and V. Valov), Topology Appl. 329 (2023).
Homological characterizations of Q-manifolds and l2-manifolds, (with V. Valov), Fund. Math., 59 (2022), 255-269.
Countable dense homogeneity and Hattori spaces, (with V. Chatyrko), Q&A, 39, no. 2 (2021), 73-87.
Admissible topologies for groups of homeomorphisms and substitutions of groups of G-spaces,(with K. Kozlov), Topology Appl., 275 (2020).
Dimension and decomposition complexity properties of tree-graded spaces, (with N. Brodskiy), preprint.
Reversible spaces and products, (with V. Chatyrko), Topology Proc., 49 (2017), 317-320.
Base normal inductive dimension I of cubes, (with K.L. Kozlov), Fundamental and Applied Math., 20 (2015), no. 2, 113-124.
Computation of inductive dimensions of product of compacta, (with K.L. Kozlov), Topology Appl., 179 (2015), 131-147.
(Non)connectedness and (non)homogeneity, (with V. Chatyrko), Topology Appl., 179 (2015), 122-130
Alexandroff manifolds and homogeneous continua, (with V. Todorov and V. Valov), Canad. Math. Bull., 57 (2014), no. 2, 335-343.
Maximal metrizable remainders of locally compact separable metrizable spaces, (with V. Chatyrko), Topology Appl. 160 (2013), 1292-1297.
On metrizable remainders of locally compact separable metrizable spaces, (with V. Chatyrko), Houston J. Math. 39 (4), 2013, 1067-1081.
The (dis)connectedness of products in the box topology, (with V. Chatyrko), Q&A 31 (2013), 11-21.
Generalized Cantor manifolds and homogeneity, (with P. Krupski, V. Valov, and V. Todorov), Houston J. Math. 38 (2012), no. 2, 583-609.
On homotopical and homological Zn, (with T. Banakh and R. Cauty), Topology Proc. 38 (2011) 29–82.
Finite-to-one maps into Euclidean manifolds and spaces with disjoint disks properties, (with M. Tuncali and V. Valov), Topology Appl. 157 (2010) 779-788.
Equivalent metrics and spans of graphs, (with L. Hoehn), Colloq. Math. 114 (2009), no. 1, 135-153.
Universal spaces, homotopy, and dimension of maps, (with V. Valov), Modern Math. and its Appl., Georgian Acad. Sci. (in Russian); transl. in J. Math. Sci. 155, Issue 4 (2008).
Michael’s problem and weakly infinite-dimensional spaces, Topology Appl. 155 (2008), no. 15, 1694-1698.
Root closed function algebras on compacta of large
dimension, (with N. Brodskiy, J. Dydak, and K. Kawamura), Proc. Am. Math. Soc. 135 (2007), 587-596.
Extension dimension and quasi-finite CW-complexes, (with V. Valov), Topology Appl. 153 (2006), no. 17, 3241-3254.
Universal absolute extensors in extension theory, (with V. Valov), Proc. Amer. Math. Soc. 134 (2006), no. 8, 2473-2478.
On two problems in extension theory, Topology Appl. 153 (2006), no. 10, 1609-1613.
On commutative and noncommutative C*-algebras with the approximate n-th root property, (with A. Chigogidze, K. Kawamura, and V. Valov), Bull. Austral. Math. Soc. 72 (2005), 197-212.
The Urysohn identity for closed subsets of some nonmetrizable manifolds, Topology Proc. 28 (2004), no. 2, 579-585.
Real rank and squaring mapping for unital C*-algebras, (with A. Chigogidze and M. Rordam). Proc. Am. Math. Soc. 132 (2004), 783-788.
Topological model categories generated by finite complexes, (with A. Chigogidze). Monatshefte fur Mathematik 139 (2003), no. 2, 129-150.
Approximations and selections of multivalued mappings of finite-dimensional spaces, (with N. Brodsky and A. Chigogidze). JP Journal of Geometry and Topology 2 (2002), no. 1, 29-73.
On [L]-homotopy groups. JP Journal of Geometry and Topology 3 (2001), no. 3, 301-310.
Topological semigroups and universal spaces related to extension dimension (with A. Chigogidze and M. Zarichnyi). Mat. Stud. 16, no. 2 (2001), 195-198.
An infinite-dimensional 4-manifold of finite cohomological dimension with the continuum hypothesis. Mat. Zametki 66 (1999), no. 5, 664-670 (Russian); English translation in Mathematical Notes 66 (1999), no. 5.
On the inductive dimension of subsets of some nonmetrizable manifolds. Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1997) no. 5, 11-14 (Russian).
Topology in North Bay: some problems in continuum theory, dimension theory, and selections, (with V. Valov and M. Tuncali), a chapter in the “Open Problems in Topology II” (Edited by Elliott Pearl), 2007, Elsevier
On extension dimension and [L]-homotopy. (2002) PhD Thesis, University of Saskatchewan.
On the inductive dimension of subsets of some nonmetrizable manifolds. (1996) MSc Thesis, Moscow State University.