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MATHEMATICA BOHEMICA, Vol. 121, No. 2, pp. 157-163, 1996
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#
Existence of quasicontinuous selections for the space $2^{\Bbb R}$

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Ivan Kupka

* Ivan Kupka*, Faculty of Mathematics and Physics, Komensky University, Mlynska dolina, 842 15 Bratislava, Slovakia

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

**Keywords:** continuous multifunction, selection, quasicontinuity

**Classification (MSC91):** 54C65, 54C08

**Full text of the article:**

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