# A. "Alex" Chigogidze

- Professor and Department Chair
- Mathematics and Statistics, UNCG
- chigogidze@uncg.edu
- (336) 334-5836
- 118 Petty Science Building
- http://www.uncg.edu/~a_chigog/

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 :

Title | Date | Views | Brief Description |
---|---|---|---|

Approximations and Selections of Multivalued Mappings of Finite-Dimensional Spaces | 2001 | 1001 | 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 | 1046 | 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 | 1853 | 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 | 1193 | 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 | 1104 | 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 | 1236 | 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 | 2331 | 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 | 1131 | 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 | 2006 | 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 | 1882 | We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces. |

Extraordinary Dimension Theories Generated by Complexes | 2003 | 2053 | 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 | 1815 | 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 | 2116 | We characterize maps between n-dimensional Nobeling manifolds that can be approximated by homeomorphisms. |

Nonmetrizable Anr's Admitting a Group Structure are Manifolds | 2005 | 1774 | 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 | 970 | 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 | 1127 | 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 | 972 | 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 | 927 | 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 | 1048 | 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 | 1000 | 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 | 1787 | 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 | 1019 | 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 | 1953 | 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 | 2174 | It is shown that every Valdivia compact group is homeomorphic to a product of metrizable compacta. |

Z-Set Unknotting in Large Cubes | 2006 | 1234 | 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 ... |