The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Currently displaying 1 – 12 of 12

Showing per page

Order by Relevance | Title | Year of publication

Maps with dimensionally restricted fibers

Vesko Valov — 2011

Colloquium Mathematicae

We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber f - 1 ( y ) belongs to a class S of spaces, then there exists an F σ -set A ⊂ X such that A ∈ S and d i m f - 1 ( y ) A = 0 for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all g C ( X , n + 1 ) .

General position properties in fiberwise geometric topology

General position properties play a crucial role in geometric and infinite-dimensional topologies. Often such properties provide convenient tools for establishing various universality results. One of well-known general position properties is DDⁿ, the property of disjoint n-cells. Each Polish L C n - 1 -space X possessing DDⁿ contains a topological copy of each n-dimensional compact metric space. This fact implies, in particular, the classical Lefschetz-Menger-Nöbeling-Pontryagin-Tolstova embedding theorem...

Spaces with fibered approximation property in dimension n

Taras BanakhVesko Valov — 2010

Open Mathematics

A metric space M is said to have the fibered approximation property in dimension n (briefly, M ∈ FAP(n)) if for any ɛ > 0, m ≥ 0 and any map g: 𝕀 m × 𝕀 n → M there exists a map g′: 𝕀 m × 𝕀 n → M such that g′ is ɛ-homotopic to g and dim g′ (z × 𝕀 n) ≤ n for all z ∈ 𝕀 m. The class of spaces having the FAP(n)-property is investigated in this paper. The main theorems are applied to obtain generalizations of some results due to Uspenskij [11] and Tuncali-Valov [10].

Classical-type characterizations of non-metrizable ANE(n)-spaces

Valentin GutevVesko Valov — 1994

Fundamenta Mathematicae

The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is L C n - 1 C n - 1 (resp., L C n - 1 ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.

Open maps having the Bula property

Valentin GutevVesko Valov — 2009

Fundamenta Mathematicae

An open continuous map f from a space X onto a paracompact C-space Y admits two disjoint closed sets F₀,F₁ ⊂ X with f(F₀) = Y = f(F₁), provided all fibers of f are infinite and C*-embedded in X. Applications are given to the existence of "disjoint" usco multiselections of set-valued l.s.c. mappings defined on paracompact C-spaces, and to special type of factorizations of open continuous maps from metrizable spaces onto paracompact C-spaces. This settles several open questions.

Skeletally Dugundji spaces

Andrzej KucharskiSzymon PlewikVesko Valov — 2013

Open Mathematics

We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the following conditions are equivalent for a given space X: (i) X is skeletally Dugundji; (ii) every compactification of X is co-absolute to a Dugundji space; (iii) every C*-embedding of the absolute p(X) in another space is strongly π-regular; (iv) X has a multiplicative lattice in the sense of Shchepin [Shchepin E.V., Topology of limit spaces with uncountable...

On dimensionally restricted maps

H. Murat TuncaliVesko Valov — 2002

Fundamenta Mathematicae

Let f: X → Y be a closed n-dimensional surjective map of metrizable spaces. It is shown that if Y is a C-space, then: (1) the set of all maps g: X → ⁿ with dim(f △ g) = 0 is uniformly dense in C(X,ⁿ); (2) for every 0 ≤ k ≤ n-1 there exists an F σ -subset A k of X such that d i m A k k and the restriction f | ( X A k ) is (n-k-1)-dimensional. These are extensions of theorems by Pasynkov and Toruńczyk, respectively, obtained for finite-dimensional spaces. A generalization of a result due to Dranishnikov and Uspenskij about...

Averaging operators and set-valued maps

Valov, Vesko — 2014

Mathematica Balkanica New Series

MSC 2010: 54C35, 54C60. We investigate maps admitting, in general, non-linear averaging operators. Characterizations of maps admitting a normed, weakly additive averaging operator which preserves max (resp., min) and weakly preserves min (resp., max) is obtained. We also describe set-valued maps into completely metrizable spaces admitting lower semi-continuous selections. As a corollary, we obtain a description of surjective maps with a metrizable kernel and complete fibers which admit...

External Characterization of I-Favorable Spaces

Valov, Vesko — 2011

Mathematica Balkanica New Series

1991 AMS Math. Subj. Class.:Primary 54C10; Secondary 54F65 We provide both a spectral and an internal characterizations of arbitrary !-favorable spaces with respect to co-zero sets. As a corollary we establish that any product of compact !-favorable spaces with respect to co-zero sets is also !-favorable with respect to co-zero sets. We also prove that every C* -embedded !-favorable with respect to co-zero sets subspace of an extremally disconnected space is extremally disconnected.

Generalized tri-quotient maps and Čech-completeness

Themba DubeVesko M. Valov — 2001

Commentationes Mathematicae Universitatis Carolinae

For a topological space X let 𝒦 ( X ) be the set of all compact subsets of X . The purpose of this paper is to characterize Lindelöf Čech-complete spaces X by means of the sets 𝒦 ( X ) . Similar characterizations also hold for Lindelöf locally compact X , as well as for countably K -determined spaces X . Our results extend a classical result of J. Christensen.

Page 1

Download Results (CSV)