# Article

Full entry | PDF   (0.2 MB)
Keywords:
function spaces; Corson-compact spaces; elementary substructures
Summary:
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].
References:
[1] Amir D., Lindenstrauß J.: The structure of weakly compact sets in Banach spaces. Ann. Math. Ser. 2 88:1 (1968). MR 0228983
[2] Archangelskij A.V.: Topologicheskie prostranstva funkcij (in Russian). Moscow, 1989.
[3] Bandlow I.: A construction in set theoretic topology by means of elementary substructures. Zeitschr. f. Math. Logik und Grundlagen d. Math. 37 (1991). MR 1270189 | Zbl 0769.54013
[4] Bandlow I.: A characterization of Corson-compact spaces. Comment. Math. Univ. Carolinae 32 (1991). MR 1159800 | Zbl 0769.54025
[5] Dow A.: An introduction to applications of elementary submodels to topology. Topology Proceedings, vol. 13, no. 1, 1988. MR 1031969 | Zbl 0696.03024
[6] Engelking R.: General Topology. Warsaw, 1977. MR 0500780 | Zbl 0684.54001
[7] Kunen K.: Set Theory. Studies in Logic 102, North Holland, 1980. MR 0597342 | Zbl 0960.03033
[8] Negrepontis S.: Banach spaces and topology. Handbook of set-theoretic topology, North Holland, 1984, 1045-1042. MR 0776642 | Zbl 0832.46005
[9] Pol R.: On pointwise and weak topology in function spaces. Preprint Nr 4/84, Warsaw, 1984.

Partner of