Geodesic
Existence of quasicontinuous selections for the space $2\sp {f R}$
Mathematica Bohemica, Tome 121 (1996) no. 2, pp. 157-163

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MR Zbl
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.
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.
DOI : 10.21136/MB.1996.126098
Classification : 54C08, 54C65
Keywords: continuous multifunction; selection; quasicontinuity 
Kupka, Ivan. Existence of quasicontinuous selections for the space $2\sp {f R}$. Mathematica Bohemica, Tome 121 (1996) no. 2, pp. 157-163. doi: 10.21136/MB.1996.126098
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