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Equiconnected spaces and Baire classification of separately continuous functions and their analogs

Olena Karlova, Volodymyr Maslyuchenko, Volodymyr Mykhaylyuk (2012)

Open Mathematics

We investigate the Baire classification of mappings f: X × Y → Z, where X belongs to a wide class of spaces which includes all metrizable spaces, Y is a topological space, Z is an equiconnected space, which are continuous in the first variable. We show that for a dense set in X these mappings are functions of a Baire class α in the second variable.

Existence of quasicontinuous selections for the space $2^{f R}$

Ivan Kupka (1996)

Mathematica Bohemica

The paper presents new quasicontinuous selection theorem for continuous multifunctions $F X ⟶ ℝ$ with closed values, $X$ being an arbitrary topological space. It is known that for $2^{ℝ}$ with the Vietoris topology there is no continuous selection. The result presented here enables us to show that there exists a quasicontinuous and upper $〈$ lower $〉$ -semicontinuous selection for this space. Moreover, one can construct a selection whose set of points of discontinuity is nowhere dense.

Expansion of $α$ -open sets and decomposition of $α$ -continuous mappings.

Rajamani, M., Bagyalakshmi, K. (2005)

International Journal of Mathematics and Mathematical Sciences

Displaying 1 – 3 of 3

Equiconnected spaces and Baire classification of separately continuous functions and their analogs

Existence of quasicontinuous selections for the space 2 f R

Expansion of α -open sets and decomposition of α -continuous mappings.

Currently displaying 1 – 3 of 3

Existence of quasicontinuous selections for the space $2^{f R}$

Expansion of $α$ -open sets and decomposition of $α$ -continuous mappings.