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 language | American English |
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Pages (from-to) | 178-198 |
Number of pages | 21 |
Journal | Topology and its Applications |
Volume | 191 |
DOIs | |
State | Published - 5 Aug 2015 |
Keywords
- Cosmic space
- Function space
- Network
- Network character
- P-space
- ℵ-space
All Science Journal Classification (ASJC) codes
- Geometry and Topology