Dr. Alex Karassev
Areas of Specialization:
General and Geometric Topology
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:
Extension dimension, C-spaces, transfinite dimension, compactifications of locally compact spaces, tilings and tiling spaces (NSERC funded)
On metrizable remainders of locally compact noncompact connected separable metrizable spaces (with V. Chatyrko), preprint
On homotopical and homological Z_n-sets (with T.Banakh and R.Cauty), Topology Proc., accepted.
Generalized Cantor manifolds and homogeneity (with P. Krupski, V. Todorov, and V. Valov), Houston J. Math., accepted.
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 with some predetermined distances, and applications to spans (with Logan Hoehn), Colloq. Math. 114 (2009), no. 1, 135-153.
Michael's problem and weakly infinite-dimensional spaces, Topology Appl., 155 (2008), no. 15, 1694-1698.
Dimension of maps, universal spaces, and homotopy (with V. Valov), Modern Math. and its Appl. Georgian Acad. Sci. (in Russian); transl. in J. Math. Sci. 155, Issue 4 (2008).
Topology in North Bay: some problems in continuum theory, dimension theory, and selections (with M .Tuncali and V. Valov), a chapter in the "Open Problems in Topology II" (Edited by Elliott Pearl), 2007, Elsevier
Root closed function algebras on compacta of large dimension (with N. Brodskiy, J. Dydak, and K. Kawamura), Proc. Am. Math. Soc., 135 (2007), no. 2, 587-596.
Extension dimension and quasi-finite CW complexes (with V. Valov), Topology Appl., 153 (2006), no. 17, 3241-3254.
On two problems in extension theory, Topology Appl. 153 (2006), no. 10, 1609-1613.
Universal absolute extensors in extension theory (with V. Valov), Proc. Amer. Math. Soc. 134 (2006), no. 8, 2473-2478.
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), no. 2, 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 fьr 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 extension dimension and [L]-homotopy (2002) Ph. D. Thesis.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, 550 - 555.
On the inductive dimension of subsets of some nonmetrizable manifolds. Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1997) no. 5, 11 - 14 (Russian); English translation in Moscow Univ. Math. Bull. 52 (1997), no. 5, 11 - 13.