# On function spaces of Corson-compact spaces

Commentationes Mathematicae Universitatis Carolinae (1994)

- Volume: 35, Issue: 2, page 347-356
- ISSN: 0010-2628

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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.

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