Geodesic
Locally solid topologies on spaces of vector-valued continuous functions
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 473-483

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

Let $X$ be a completely regular Hausdorff space and $E$ a real normed space. We examine the general properties of locally solid topologies on the space $C_b(X,E)$ of all $E$-valued continuous and bounded functions from $X$ into $E$. The mutual relationship between locally solid topologies on $C_b(X,E)$ and $C_b(X)$ $(=C_b(X,\Bbb R))$ is considered. In particular, the mutual relationship between strict topologies on $C_b(X)$ and $C_b(X,E)$ is established. It is shown that the strict topology $\beta _\sigma(X,E)$ (respectively $\beta _\tau(X,E)$) is the finest $\sigma $-Dini topology (respectively Dini topology) on $C_b(X,E)$. A characterization of $\sigma $-Dini and Dini topologies on $C_b(X,E)$ in terms of their topological duals is given.
Classification : 46A03, 46E05, 46E10, 46E40, 47A70
Keywords: vector-valued continuous functions; strict topologies; locally solid topologies; Dini topologies 
@article{CMUC_2002__43_3_a6,
     author = {Nowak, Marian and Rzepka, Aleksandra},
     title = {Locally solid topologies on spaces of vector-valued continuous functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {473--483},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2002},
     mrnumber = {1920522},
     zbl = {1068.46023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002__43_3_a6/}
}
TY  - JOUR
AU  - Nowak, Marian
AU  - Rzepka, Aleksandra
TI  - Locally solid topologies on spaces of vector-valued continuous functions
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2002
SP  - 473
EP  - 483
VL  - 43
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2002__43_3_a6/
LA  - en
ID  - CMUC_2002__43_3_a6
ER  - 
%0 Journal Article
%A Nowak, Marian
%A Rzepka, Aleksandra
%T Locally solid topologies on spaces of vector-valued continuous functions
%J Commentationes Mathematicae Universitatis Carolinae
%D 2002
%P 473-483
%V 43
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2002__43_3_a6/
%G en
%F CMUC_2002__43_3_a6
Nowak, Marian; Rzepka, Aleksandra. Locally solid topologies on spaces of vector-valued continuous functions. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 473-483. http://geodesic.mathdoc.fr/item/CMUC_2002__43_3_a6/