2018
Том 70
№ 11

All Issues

Karlova O. O.

Articles: 5
Article (Ukrainian)

Upper and lower Lebesgue classes of multivalued functions of two variables

Karlova O. O., Mykhailyuk V. V.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 8. - pp. 1097-1106

We introduce a functional Lebesgue classification of multivalued mappings and obtain results on upper and lower Lebesgue classifications of multivalued mappings $F : X \times Y \multimap Z$ for wide classes of spaces $X, Y$ and $Z$.

Brief Communications (Ukrainian)

Cross Topology and Lebesgue Triples

Karlova O. O., Mykhailyuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 5. - pp. 722–727

The cross topology γ on the product of topological spaces X and Y is the collection of all sets G ⊆ X × Y such that the intersections of G with every vertical line and every horizontal line are open subsets of the vertical and horizontal lines, respectively. For the spaces X and Y from a class of spaces containing all spaces \( {{\mathbb{R}}^n} \) , it is shown that there exists a separately continuous function f : X × Y → (X × Y, γ) which is not a pointwise limit of a sequence of continuous functions. We also prove that each separately continuous function is a pointwise limit of a sequence of continuous functions if it is defined on the product of a strongly zero-dimensional metrizable space and a topological space and takes values in an arbitrary topological space.

Article (Ukrainian)

Weak local homeomorphisms and B-favorable spaces

Karlova O. O., Mykhailyuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1189–1195

Let X and Y be topological spaces such that every mapping f : XY for which the set f - 1(G) is an f σ -set in X for any set G open in Y can be represented as a pointwise limit of continuous mappings fn : XY. The question of subspaces Z of the space Y for which mappings f : XZ have the same property is investigated.

Article (Ukrainian)

Separately continuous mappings with values in nonlocally convex spaces

Karlova O. O., Maslyuchenko V. K.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1639–1646

We prove that the collection $(X, Y, Z)$ is the Lebesgue triple if $X$ is a metrizable space, $Y$ is a perfectly normal space, and $Z$ is a strongly $\sigma$-metrizable topological vector space with stratification $(Z_m)^{\infty}_{m=1}$, where, for every $m \in \mathbb{N}$, $Z_m$ is a closed metrizable separable subspace of $Z$ arcwise connected and locally arcwise connected.

Brief Communications (Ukrainian)

Functions of the first Baire class with values in metrizable spaces

Karlova O. O., Mykhailyuk V. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 4. - pp. 568–572

We show that every mapping of the first functional Lebesgue class that acts from a topological space into a separable metrizable space that is linearly connected and locally linearly connected belongs to the first Baire class. We prove that the uniform limit of functions of the first Baire class $f_n : \; X \rightarrow Y$ belongs to the first Baire class if $X$ is a topological space and $Y$ is a metric space that is linearly connected and locally linearly connected.