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

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

2012-02-14

arxiv.org/abs/1202.3127v1

Mathematics

General Topology

Scientific paper

In this note, we shall generalize the notion of a $P$-space to proximity spaces and investigate the basic properties of $P$-proximities. We therefore define a $P$-proximity to be a proximity where if $A_{n}\prec B$ for all $n\in\mathbb{N}$, then $\bigcup_{n}A_{n}\prec B$. It turns out that the class of $P$-proximities is equivalent to the class of $\sigma$-algebras. Furthermore, the $P$-proximity coreflection of a proximity space is the $\sigma$-algebra of proximally Baire sets.

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