2004•Houston journal of mathematicsRequires access

Subspaces of Absolutely Star-Lindelöf Spaces

Yan-Kui Song, Wei-Xue Shi

Abstract

In this paper, we consider two questions on absolute star-Lindelofness and star-Lindelofness: (1) Whether every Tychonoff star-Lindelof space can be embedded into some Tychonoff absolutely star-Lindelof space as a closed subspace or as a closed Gd-subspace; (2) Characterize the Tychonoff star-Lindelof spaces which can be embedded as regular closed subspaces into Tychonoff absolutely star-Lindelof spaces. We proved that the answer to the first question is YES in general. For the second question we give a complete solution.

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Key concepts: Tychonoff space, Linear subspace, Mathematics, Star (game theory), Subspace topology, Space (punctuation), Pure mathematics, Absolute continuity