A Generalization of the notion of a P-space to proximity spaces

2012/02/14 by Joseph Van Name, Van Name, Joseph
Computer Science · Decision Sciences · Mathematics · #28A05 #54E05 #54G10 #Advanced Algebra and Logic #Advanced Banach Space Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1202.3127

openalex publication_date 2012/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we shall generalize the notion of a P-space to proximity spaces and investigate the basic properties of these proximities. We therefore define a P_ℵ₁-proximity to be a proximity where if A_n\prec B for all n∈ℕ, then \bigcup_nA_n\prec B. It turns out that the class of P_ℵ₁-proximities is equivalent to the class of σ-algebras. Furthermore, the P_ℵ₁-proximity coreflection of a proximity space is the σ-algebra of proximally Baire sets.

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