2003•Czech digital mathematics libraryOpen access

Closed subsets of absolutely star-Lindelöf spaces II

Yan-Kui Song

Abstract

summary:In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed $G_{\delta}$ subspace.

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Key concepts: Tychonoff space, Mathematics, Hausdorff space, Subspace topology, Urysohn and completely Hausdorff spaces, Regular space, Star (game theory), Normal space