Connectedness and strong semicontinuity
Connectivity functions defined on
Connectivity of diagonal products of Baire one functions
We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.
Continuity of semigroup actions.
Continuity properties up to a countable partition.
Approximation and rigidity properties in renorming constructions are characterized with some classes of simple maps. Those maps describe continuity properties up to a countable partition. The construction of such kind of maps can be done with ideas from the First Lebesgue Theorem. We present new results on the relationship between Kadec and locally uniformly rotund renormability as well as characterizations of the last one with the simple maps used here.
Continuous depencence of on as a selection property.
Contra--continuous and almost contra--continuous.
Contra-continuous functions and strongly -closed spaces.
Contra-pre-semi-continuous functions.
Contra-semicontinuous functions.
Diagonals of separately continuous functions of variables with values in strongly -metrizable spaces
We prove the result on Baire classification of mappings which are continuous with respect to the first variable and belongs to a Baire class with respect to the second one, where is a -space, is a topological space and is a strongly -metrizable space with additional properties. We show that for any topological space , special equiconnected space and a mapping of the -th Baire class there exists a strongly separately continuous mapping with the diagonal . For wide classes of spaces...
Equiconnected spaces and Baire classification of separately continuous functions and their analogs
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
The paper presents new quasicontinuous selection theorem for continuous multifunctions with closed values, being an arbitrary topological space. It is known that for with the Vietoris topology there is no continuous selection. The result presented here enables us to show that there exists a quasicontinuous and upperlower-semicontinuous selection for this space. Moreover, one can construct a selection whose set of points of discontinuity is nowhere dense.
Expansion of -open sets and decomposition of -continuous mappings.
Fixed point index for open sets in euclidean spaces
Fixed point theorems and almost continuity
Function spaces for somewhat continuous functions
Functions and Baire spaces
Fuzzy -open sets and fuzzy -continuity in fuzzifying topology.
Fuzzy pairwise almost strong precontinuity