23 papers
On commutative and non-commutative C*-algebras with the approximate n-th root property
A. Chigogidze, A. Karasev, K. Kawamura +1
We say that a C*-algebra X has the approximate n-th root property (n\geq 2) if for every a\in X with ||a||\leq 1 and every ε>0 there exits b\in X such that ||b||\leq 1 and ||a-b^n|…
Nonmetrizable ANR's admitting a group structure are manifolds
A. Chigogidze
It is shown that a nonmetrizable ANR-space of weight , admitting a group structure, is (topologically) an $\text{\f R}^τ$-manifold.
Extraordinary dimension of maps
A. Chigogidze, V. Valov
We establish a characterization of the extraordinary dimension of perfect maps between metrizable spaces.
Sections of Serre fibrations with low-dimensional fibers
N. Brodsky, A. Chigogidze, E. V. Shchepin
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…
C*-algebras of infinite real rank
A. Chigogidze, V. Valov
We introduce the notion of weakly (strongly) infinite real rank for unital -algebras. It is shown that a compact space is weakly (strongly) infine-dimensional if and…
Topological model categories generated by finite complexes
A. Chigogidze, A. Karasev
Our main result states that for each finite complex L the category of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equiv…