On function spaces of Corson-compact spaces
Commentationes Mathematicae Universitatis Carolinae (1994)
- Volume: 35, Issue: 2, page 347-356
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topBandlow, Ingo. "On function spaces of Corson-compact spaces." Commentationes Mathematicae Universitatis Carolinae 35.2 (1994): 347-356. <http://eudml.org/doc/247568>.
@article{Bandlow1994,
abstract = {We apply elementary substructures to characterize the space $C_p(X)$ for Corson-compact spaces. As a result, we prove that a compact space $X$ is Corson-compact, if $C_p(X)$ can be represented as a continuous image of a closed subspace of $(L_\{\tau \})^\{\omega \}\times Z$, where $Z$ is compact and $L_\{\tau \}$ denotes the canonical Lindelöf space of cardinality $\tau $ with one non-isolated point. This answers a question of Archangelskij [2].},
author = {Bandlow, Ingo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {function spaces; Corson-compact spaces; elementary substructures; Corson-compacts; Eberlein-compacts; Corson-compact spaces; countable elementary submodels},
language = {eng},
number = {2},
pages = {347-356},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On function spaces of Corson-compact spaces},
url = {http://eudml.org/doc/247568},
volume = {35},
year = {1994},
}
TY - JOUR
AU - Bandlow, Ingo
TI - On function spaces of Corson-compact spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 347
EP - 356
AB - We apply elementary substructures to characterize the space $C_p(X)$ for Corson-compact spaces. As a result, we prove that a compact space $X$ is Corson-compact, if $C_p(X)$ can be represented as a continuous image of a closed subspace of $(L_{\tau })^{\omega }\times Z$, where $Z$ is compact and $L_{\tau }$ denotes the canonical Lindelöf space of cardinality $\tau $ with one non-isolated point. This answers a question of Archangelskij [2].
LA - eng
KW - function spaces; Corson-compact spaces; elementary substructures; Corson-compacts; Eberlein-compacts; Corson-compact spaces; countable elementary submodels
UR - http://eudml.org/doc/247568
ER -
References
top- Amir D., Lindenstrauß J., The structure of weakly compact sets in Banach spaces, Ann. Math. Ser. 2 88:1 (1968). (1968) MR0228983
- Archangelskij A.V., Topologicheskie prostranstva funkcij (in Russian), Moscow, 1989.
- Bandlow I., A construction in set theoretic topology by means of elementary substructures, Zeitschr. f. Math. Logik und Grundlagen d. Math. 37 (1991). (1991) Zbl0769.54013MR1270189
- Bandlow I., A characterization of Corson-compact spaces, Comment. Math. Univ. Carolinae 32 (1991). (1991) Zbl0769.54025MR1159800
- Dow A., An introduction to applications of elementary submodels to topology, Topology Proceedings, vol. 13, no. 1, 1988. Zbl0696.03024MR1031969
- Engelking R., General Topology, Warsaw, 1977. Zbl0684.54001MR0500780
- Kunen K., Set Theory, Studies in Logic 102, North Holland, 1980. Zbl0960.03033MR0597342
- Negrepontis S., Banach spaces and topology, Handbook of set-theoretic topology, North Holland, 1984, 1045-1042. Zbl0832.46005MR0776642
- Pol R., On pointwise and weak topology in function spaces, Preprint Nr 4/84, Warsaw, 1984.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.