Geodesic
Selections and representations of multifunctions in paracompact spaces
Studia Mathematica, Tome 102 (1992) no. 3, pp. 209-216

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let (X,T) be a paracompact space, Y a complete metric space, $F:X → 2^Y$ a lower semicontinuous multifunction with nonempty closed values. We prove that if $T^+$ is a (stronger than T) topology on X satisfying a compatibility property, then F admits a $T^+$-continuous selection. If Y is separable, then there exists a sequence $(f_n)$ of $T^+$-continuous selections such that $F(x)=\overline{{f_n(x);n ≥ 1}}$ for all x ∈ X. Given a Banach space E, the above result is then used to construct directionally continuous selections on arbitrary subsets of ℝ × E.
DOI : 10.4064/sm-102-3-209-216
Keywords: directionally continuous selections

Alberto Bressan 1

1 
@article{10_4064_sm_102_3_209_216,
     author = {Alberto Bressan},
     title = {Selections and representations of multifunctions in paracompact spaces},
     journal = {Studia Mathematica},
     pages = {209--216},
     publisher = {mathdoc},
     volume = {102},
     number = {3},
     year = {1992},
     doi = {10.4064/sm-102-3-209-216},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-102-3-209-216/}
}
TY  - JOUR
AU  - Alberto Bressan
TI  - Selections and representations of multifunctions in paracompact spaces
JO  - Studia Mathematica
PY  - 1992
SP  - 209
EP  - 216
VL  - 102
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm-102-3-209-216/
DO  - 10.4064/sm-102-3-209-216
LA  - en
ID  - 10_4064_sm_102_3_209_216
ER  - 
%0 Journal Article
%A Alberto Bressan
%T Selections and representations of multifunctions in paracompact spaces
%J Studia Mathematica
%D 1992
%P 209-216
%V 102
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm-102-3-209-216/
%R 10.4064/sm-102-3-209-216
%G en
%F 10_4064_sm_102_3_209_216
Alberto Bressan. Selections and representations of multifunctions in paracompact spaces. Studia Mathematica, Tome 102 (1992) no. 3, pp. 209-216. doi: 10.4064/sm-102-3-209-216

Cité par Sources :