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].
@article{118673,
author = {Ingo Bandlow},
title = {On function spaces of Corson-compact spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {35},
year = {1994},
pages = {347-356},
zbl = {0835.54016},
mrnumber = {1286581},
language = {en},
url = {http://dml.mathdoc.fr/item/118673}
}
Bandlow, Ingo. On function spaces of Corson-compact spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 347-356. http://gdmltest.u-ga.fr/item/118673/
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