Work

Countably Compact Extensions and Cardinal Characteristics of the Continuum

Year: 2025

Type: article

Abstract: In this paper, we show that the existence of certain first-countable compact-like extensions is equivalent to the equality between corresponding cardinal characteristics of the continuum. For instance, $\mathfrak b=\mathfrak s=\mathfrak c$ if and only if every regular first-countable space of weight $< \mathfrak c$ can be densely embedded into a regular first-countable countably compact space.

Source: Journal of Symbolic Logic

DOI: 10.1017/jsl.2025.13

Authors: SERHII BARDYLA, PETER NYIKOS, LYUBOMYR ZDOMSKYY

Institutions: University of Vienna, University of South Carolina

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: Austrian Science Fund