Displaying similar documents to “On generalized Blumberg sets”

Existence of quasicontinuous selections for the space 2 f R

Ivan Kupka (1996)

Mathematica Bohemica

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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.

Quasicontinuity and related properties of functions and multivalued maps

Janina Ewert (1995)

Mathematica Bohemica

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The main results presented in this paper concern multivalued maps. We consider the cliquishness, quasicontinuity, almost continuity and almost quasicontinuity; these properties of multivalued maps are characterized by the analogous properties of some real functions. The connections obtained are used to prove decomposition theorems for upper and lower quasicontinuity.