Ján Borsík (2010)
Open Mathematics
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Let C(f), Q(f), E(f) and A(f) be the sets of all continuity, quasicontinuity, upper and lower quasicontinuity and cliquishness points of a real function f: X → ℝ, respectively. The triplets (C(f),Q(f),A(f)), (C(f),E(f),A(f) and (Q(f),E(f),A(f)are characterized for functions defined on Baire metric spaces without isolated points.
Ľubica Holá (2013)
Open Mathematics
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We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
Milan Matejdes (1993)
Mathematica Bohemica
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The purpose of this paper is to introduce a definition of cliquishness for multifunctions and to study the search for cliquish, quasi-continuous and Baire measurable selections of compact valued multifunctions. A correction as well as a generalization of the results of [5] are given.
Pavel Kostyrko (1980)
Mathematica Slovaca
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Milan Matejdes (1991)
Mathematica Bohemica
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The purpose of this paper is the investigation of the necessary and sufficient conditions under which a given multifunctions admits a cliquish and measurable selection. Our investigation also covers the search for quasicontinuous selections for multifunctions which are continuous with respect to the generalized notion of the semi-quasicontinuity.