On P-spaces and related concepts

Research output: Contribution to journalArticlepeer-review

Abstract

The concept of the strong Pytkeev property, recently introduced by Tsaban and Zdomskyy in [32], was successfully applied to the study of the space Cc(X) of all continuous real-valued functions with the compact-open topology on some classes of topological spaces X including Čech-complete Lindelöf spaces. Being motivated also by several results providing various concepts of networks we introduce the class of P-spaces strictly included in the class of ℵ-spaces. This class of generalized metric spaces is closed under taking subspaces, topological sums and countable products and any space from this class has countable tightness. Every P-space X has the strong Pytkeev property. The main result of the present paper states that if X is an ℵ0-space and Y is a P-space, then the function space Cc(X, Y) has the strong Pytkeev property. This implies that for a separable metrizable space X and a metrizable topological group G the space Cc(X, G) is metrizable if and only if it is Fréchet-Urysohn. We show that a locally precompact group G is a P-space if and only if G is metrizable.

Original languageAmerican English
Pages (from-to)178-198
Number of pages21
JournalTopology and its Applications
Volume191
DOIs
StatePublished - 5 Aug 2015

Keywords

  • Cosmic space
  • Function space
  • Network
  • Network character
  • P-space
  • ℵ-space

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

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