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1
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Closed graph multi-selections

100%
Gutev V.
Fundamenta Mathematicae
|
2011
|
tom 211
|
nr 1
85-99
EN
A classical Lefschetz result about point-finite open covers of normal spaces is generalised by showing that every lower semi-continuous mapping from a normal space into the nonempty compact subsets of a metrizable space admits a closed graph multi-selection. Several applications are given as well.
2
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Consonance and Cantor set-selectors

100%
Gutev V.
Open Mathematics
|
2013
|
tom 11
|
nr 2
341-348
EN
It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.
3
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Strongly paracompact metrizable spaces

100%
Gutev V.
Colloquium Mathematicum
|
2016
|
tom 144
|
nr 2
203-214
EN
Strongly paracompact metrizable spaces are characterized in terms of special S-maps onto metrizable non-Archimedean spaces. A similar characterization of strongly metrizable spaces is obtained as well. The approach is based on a sieve-construction of "metric"-continuous pseudo-sections of lower semicontinuous mappings.
4
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Weak orderability of second countable spaces

100%
Gutev V.
Fundamenta Mathematicae
|
2007
|
tom 196
|
nr 3
275-287
EN
We demonstrate that a second countable space is weakly orderable if and only if it has a continuous weak selection. This provides a partial positive answer to a question of van Mill and Wattel.
5
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Open maps having the Bula property

64%
Gutev V., Valov V.
Fundamenta Mathematicae
|
2009
|
tom 205
|
nr 2
91-104
EN
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.
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