A. "Alex" Chigogidze

H.Barton Excellence Professor and Department Head (2003) D.Sci. in Mathematics, Moscow University (1990); Ph.D. in Mathematics, Tbilisi University (1980). Research: Topology, Abstract Homotopy Theory, Topological Algebra, Functional Analysis. Teaching: Topology, calculus. Office: Petty 118

There are 25 included publications by A. "Alex" Chigogidze :

TitleDateViewsBrief Description
Approximations and Selections of Multivalued Mappings of Finite-Dimensional Spaces 2001 414 We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
Bounded Rank of C* -Algebras 2002 343 We introduce a concept of the bounded rank (with respect to a positive constant) for unital C * -algebras as a modification of the usual real rank and present a series of conditions insuring that bounded and real ranks coincide. These observations a...
C*-Algebras of Infinite Real Rank 2002 350 We introduce the notion of weakly (strongly) infinite real rank for unital C *-algebras. It is shown that a compact space X is weakly (strongly) infine-dimensional if and only if C(X) has weakly (strongly) infinite real rank. Some other properties o...
Characterizing the Topology of Pseudo-Boundaries of Euclidean Spaces 1999 431 We give a topological characterization of the n-dimensional pseudoboundary of the (2n + 1)-dimensional Euclidean space.
Complemented Subspaces of Locally Convex Direct Sum of Banach Spaces 2000 431 We show that a complemented subspace of a locally convex direct sum of an uncountable collection of Banach spaces is a locally convex direct sum of complemented subspaces of countable subsums. As a corollary we prove that a complemented subspace of a...
Complemented Subspaces of Productsof Banach Spaces 2000 462 We show that complemented subspaces of uncountable products of Banach spaces are products of complemented subspaces of countable subproducts.
Extension Dimension and C-Spaces 2002 332 Some generalizations of the classical Hurewicz formula are obtained for extension dimension and C-spaces. A characterization of the class of metrizable spaces which are absolute neighborhood extensors for all metrizable C-spaces is also given.
Extension Dimension and Refinable Maps 1999 413 Extension dimension is characterized in terms of ?-maps. We apply this result to prove that extension dimension is preserved by refinable maps between metrizable spaces. It is also shown that refinable maps preserve some infinite-dimensional propert...
Extension Dimensional Approximation Theorem 2001 445 It is known that if an upper semicontinuous multivalued mapping F : X ? Y , defined on an n-dimensional compactum X, has UV n-1-point images, then every neighbourhood of the graph of F (in the product X×Y ) contains the graph of a single-valued conti...
Extraordinary Dimension of Maps 2003 322 We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces.
Extraordinary Dimension Theories Generated by Complexes 2003 321 We study the extraordinary dimension function dimL introduced by ? S?cepin. An axiomatic characterization of this dimension function is obtained. We also introduce inductive dimensions indL and IndL and prove that for separable metrizable spaces all ...
Hurewicz theorem for Extension Dimension 2002 452 We prove a new selection theorem for multivalued mappings of C-space. Using this theorem we prove extension dimensional version of Hurewicz theorem for a closed mapping f : X ? Y of k-space X onto paracompact C-space Y : if for finite CW-complex M we...
Near-Homeomorphisms of Nobeling Manifolds 2007 376 We characterize maps between n-dimensional Nobeling manifolds that can be approximated by homeomorphisms.
Nonmetrizable Anr's Admitting a Group Structure are Manifolds 2005 342 It is shown that a nonmetrizable ANR-space of weight ?, admitting a group structure, is (topologically) an R -manifold
Notes on Two Conjectures in Extension Theory 2002 339 It is noted that conjectures about the non-existence of universal compacta and compactifications of the given extension dimension for non finitely dominated complexes are not valid for all CW complexes of the form L ? S2, where L is of finite type an...
On Commutative and Non-Commutative C* -Algebras with the Approximate n-th Rott Property 2005 346 We say that a C *-algebra X has the approximate n-th root property (n = 2) if for every a ? X with kak = 1 and every " > 0 there exits b ? X such that kbk = 1 and ka - bnk < ". Some properties of commutative and non-commutative C *-algebras having th...
Real Rank and Squaring Mapping for Unital C *-Algebras 2002 347 It is proved that if X is a compact Hausdorff space of Lebesgue dimension dim(X), then the squaring mapping m: (C(X)sa)m ? C(X)+, defined by m(f1, . . . , fm) = Pm i=1 f2 i , is open if and only if m-1 = dim(X). Hence the Lebesgue dimension of X ca...
Retracts of Sigma-Products of Hilbert Cubes 2006 294 We consider the sigma-product of the !1-power of the Hilbert cube. This space is characterized among its retracts as the only one without G-points.
Sections of Serre Fibrations with Low-Dimensional Fibers 2002 344 It was proved by H. Whitney in 1933 that it is possible to mark a point in all curves in a continuous way. The main result of this paper extends the Whitney theorem to dimensions 2 and 3. Namely, we prove that it is possible to choose a point contin...
Topological AE(0)-Groups 2000 313 We investigate topological AE(0)-groups class of which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of an universal AE(0)-group of a given weight as well as the existence of an uni...
Topological Model Categories Generated By Finite Complexes 2002 298 Our main result states that for each finite complex L the category TOP of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equivalences are precisely maps which induce isomorphisms of all [L]-homotopy grou...
Topological Semigroups and Universal Spaces Related to Extension Dimenion 2001 398 It is proved that there is no structure of left (right) cancelative semigroup on [L]-dimensional universal space for the class of separable compact spaces of extensional dimension  [L]. Besides, we note that the homeomorphism group of [L]-dimension...
Universal C *-Algebra of Real Rank zero 2000 381 It is well-known that every commutative separable unital C *-algebra of real rank zero is a quotient of the C *-algebra of all compex continous functions defined on the Cantor cube. We prove a non-commutative version of this result by showing that th...
Valdivia Compact Groups are Products 2007 403 It is shown that every Valdivia compact group is homeomorphic to a product of metrizable compacta.
Z-Set Unknotting in Large Cubes 2006 377 We introduce a notion of a Z -set and prove various versions of Z -set unknotting theorems in the Tychonov cube of weight of r. These results are applied to the study of Sigma-products. In particular, we obtain a topological characterization of ...