Geodesic
A note on linear mappings between function spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 4, pp. 711-715.

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

Arhangel'ski\v{\i} proved that if $X$ and $Y$ are completely regular spaces such that ${C_p (X)}$ and ${C_p (Y)}$ are linearly homeomorphic, then $X$ is pseudocompact if and only if $Y$ is pseudocompact. In addition he proved the same result for compactness, $\sigma $-compactness and realcompactness. In this paper we prove that if $\phi : {C_p (X)} \rightarrow {C_p (X)}$ is a continuous linear surjection, then $Y$ is pseudocompact provided $X$ is and if $\phi $ is a continuous linear injection, then $X$ is pseudocompact provided $Y$ is. We also give examples that both statements do not hold for compactness, $\sigma $-compactness and realcompactness.
Classification : 54C35, 57N17
Keywords: function space; topology of pointwise convergence 
@article{CMUC_1993__34_4_a9,
     author = {Baars, Jan},
     title = {A note on linear mappings between function spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {711--715},
     publisher = {mathdoc},
     volume = {34},
     number = {4},
     year = {1993},
     mrnumber = {1263800},
     zbl = {0787.54017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1993__34_4_a9/}
}
TY  - JOUR
AU  - Baars, Jan
TI  - A note on linear mappings between function spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1993
SP  - 711
EP  - 715
VL  - 34
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_1993__34_4_a9/
LA  - en
ID  - CMUC_1993__34_4_a9
ER  - 
%0 Journal Article
%A Baars, Jan
%T A note on linear mappings between function spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 1993
%P 711-715
%V 34
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_1993__34_4_a9/
%G en
%F CMUC_1993__34_4_a9
Baars, Jan. A note on linear mappings between function spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 4, pp. 711-715. http://geodesic.mathdoc.fr/item/CMUC_1993__34_4_a9/