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

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_21136_MB_1996_126098,
     author = {Kupka, Ivan},
     title = {Existence of quasicontinuous selections for the space $2\sp {f R}$},
     journal = {Mathematica Bohemica},
     pages = {157--163},
     publisher = {mathdoc},
     volume = {121},
     number = {2},
     year = {1996},
     doi = {10.21136/MB.1996.126098},
     mrnumber = {1400608},
     zbl = {0863.54014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.126098/}
}
TY  - JOUR
AU  - Kupka, Ivan
TI  - Existence of quasicontinuous selections for the space $2\sp {f R}$
JO  - Mathematica Bohemica
PY  - 1996
SP  - 157
EP  - 163
VL  - 121
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.126098/
DO  - 10.21136/MB.1996.126098
LA  - en
ID  - 10_21136_MB_1996_126098
ER  - 
%0 Journal Article
%A Kupka, Ivan
%T Existence of quasicontinuous selections for the space $2\sp {f R}$
%J Mathematica Bohemica
%D 1996
%P 157-163
%V 121
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.126098/
%R 10.21136/MB.1996.126098
%G en
%F 10_21136_MB_1996_126098
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. http://geodesic.mathdoc.fr/articles/10.21136/MB.1996.126098/

Cité par Sources :