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2008•Czechoslovak Mathematical JournalOpen access

Remarks on discretely absolutely star-Lindelöf spaces

Yan-Kui Song

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Abstract

In this paper, we prove the following statements (1) There exists a Hausdorff Lindelöf space X such that the Alexandroff duplicate A(X) of X is not discretely absolutely star-Lindelöf. (2) If X is a regular Lindelöf space, then A(X) is discretely absolutely star-Lindelöf. (3) If X is a normal discretely star-Lindelöf space with e(X) < ω 1, then A(X) is discretely absolutely star-Lindelöf.

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What this paper is about

In this paper, we prove the following statements (1) There exists a Hausdorff Lindelöf space X such that the Alexandroff duplicate A(X) of X is not discretely absolutely star-Lindelöf. (2) If X is a regular Lindelöf space, then A(X) is discretely absolutely star-Lindelöf. (3) If X is a normal discretely star-Lindelöf space with e(X) < ω 1, then A(X) is discretely absolutely star-Lindelöf.

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Available abstract

In this paper, we prove the following statements (1) There exists a Hausdorff Lindelöf space X such that the Alexandroff duplicate A(X) of X is not discretely absolutely star-Lindelöf. (2) If X is a regular Lindelöf space, then A(X) is discretely absolutely star-Lindelöf. (3) If X is a normal discretely star-Lindelöf space with e(X) < ω 1, then A(X) is discretely absolutely star-Lindelöf.

Key concepts: Mathematics, Star (game theory), Absolute continuity, Hausdorff space, Space (punctuation), Pure mathematics, Combinatorics, Mathematical analysis

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