Variations on ω-boundedness

Juhász, István and van Mill, J. and Weiss, W. (2013) Variations on ω-boundedness. ISRAEL JOURNAL OF MATHEMATICS, 194 (2). pp. 745-766. ISSN 0021-2172

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Abstract

Let P be a property (or, equivalently, a class) of topological spaces. A space X is called P-bounded if every subspace of X with (or in) P has compact closure. Thus, countable-bounded has been known as ω-bounded and (σ-compact)-bounded as strongly ω-bounded. In this paper we present a systematic study of the interrelations of these two known "boundedness" concepts with P-boundedness where P is one of the further countability properties weakly Lindelöf, Lindelöf, hereditarily Lindelöf, and ccc. © 2012 Hebrew University Magnes Press.

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