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General and Set-Theoretic Topology

General/ST Session #4 #1

Subevent of General/ST Session #4

Central Time (US & Canada)

Starts at: 2025-08-13 08:30AM

Ends at: 2025-08-13 08:50AM

Cardinal bounds in spaces with a π-base whose elements have an H-closed closure

Davide Giacopello ⟨dagiacopello@unime.it⟩

Abstract:

We deal with the class of Hausdorff spaces having a π-base whose elements have an H-closed closure. Carlson proved that X2wL(X)ψc(X)t(X) for every quasiregular space X with a π-base whose elements have an H-closed closure. We provide an example of a space X having a π-base whose elements have an H-closed closure which is not quasiregular (neither Urysohn) such that X>2wL(X)χ(X) (hence, X>2wL(X)ψc(X)t(X)). Still in the class of spaces with a π-base whose elements have an H-closed closure, we establish the bound X2wL(X)k(X) for Urysohn spaces and we give an example of an Urysohn space Z such that k(Z)<χ(Z). Lastly, we present some equivalent conditions to the Martin’s Axiom involving spaces with a π-base whose elements have an H-closed closure and, additionally, we prove that if a quasiregular space has a π-base whose elements have an H-closed closure then such a space is Baire.

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