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On weak $κ$ -metric

Bandlow, Ingo — 1984

Proceedings of the 12th Winter School on Abstract Analysis

A characterization of Corson-compact spaces

Ingo Bandlow — 1991

Commentationes Mathematicae Universitatis Carolinae

We characterize Corson-compact spaces by means of countable elementary substructures.

On function spaces of Corson-compact spaces

Ingo Bandlow — 1994

Commentationes Mathematicae Universitatis Carolinae

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 ${(L_{τ})}^{ω} \times Z$ , where $Z$ is compact and $L_{τ}$ denotes the canonical Lindelöf space of cardinality $τ$ with one non-isolated point. This answers a question of Archangelskij [2].