Existence of quasicontinuous selections for the space $2^{fR}$

Kupka, Ivan. "Existence of quasicontinuous selections for the space $2^{f R}$." Mathematica Bohemica 121.2 (1996): 157-163. <http://eudml.org/doc/247949>.

@article{Kupka1996,
abstract = {The paper presents new quasicontinuous selection theorem for continuous multifunctions $F X \longrightarrow \mathbb \{R\}$ with closed values, $X$ being an arbitrary topological space. It is known that for $2^\{\mathbb \{R\}\}$ 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.},
author = {Kupka, Ivan},
journal = {Mathematica Bohemica},
keywords = {continuous multifunction; selection; quasicontinuity; continuous multifunction; selection; quasicontinuity},
language = {eng},
number = {2},
pages = {157-163},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence of quasicontinuous selections for the space $2^\{f R\}$},
url = {http://eudml.org/doc/247949},
volume = {121},
year = {1996},
}

TY - JOUR
AU - Kupka, Ivan
TI - Existence of quasicontinuous selections for the space $2^{f R}$
JO - Mathematica Bohemica
PY - 1996
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 121
IS - 2
SP - 157
EP - 163
AB - The paper presents new quasicontinuous selection theorem for continuous multifunctions $F X \longrightarrow \mathbb {R}$ with closed values, $X$ being an arbitrary topological space. It is known that for $2^{\mathbb {R}}$ 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.
LA - eng
KW - continuous multifunction; selection; quasicontinuity; continuous multifunction; selection; quasicontinuity
UR - http://eudml.org/doc/247949
ER -