TL;DR
This paper generalizes existing results on the order of π-bases in compact spaces and addresses open questions related to point-countable π-bases in first-countable and similar spaces.
Contribution
It extends Shapirovskii's results on π-bases and provides answers to open questions posed by Tkachuk regarding point-countable π-bases.
Findings
Extended bounds on the order of π-bases in compact spaces.
Resolved open questions about point-countable π-bases in specific classes of spaces.
Enhanced understanding of the structure of π-bases in topological spaces.
Abstract
We extend the scope of B. Shapirovskii's results [B.E Shapirovskii, "Cardinal invariants in Compact Hausdorff Spaces," Amer. Math. Soc. Transl. (2) Vol. 134, 1987, pp. 93-118] on the order of -bases in compact spaces and answer some questions of V. Tkachuk in [V.V. Tkachuk, "Point-countable pi-bases in first-countable and similar spaces," Fund. Math. 186 (2005), pp.55-69].
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Taxonomy
Topicsgraph theory and CDMA systems · Coding theory and cryptography · Rings, Modules, and Algebras