Variations on Ω - Boundedness
نویسندگان
چکیده
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. ∗ The first author was supported by OTKA grants no. 68262 and 83726. ∗∗ The second and third author are pleased to thank the Alfréd Rényi Institute of Mathematics for generous hospitality. Received May 5, 2011 and in revised form September 28, 2011
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