Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4658209 | Topology and its Applications | 2015 | 23 Pages |
Abstract
A regular topological space X is defined to be a P0-space if it has countable Pytkeev network. A network N for X is called a Pytkeev network if for any point xâX, neighborhood OxâX of x and subset AâX accumulating at a x there is a set NâN such that NâOx and Nâ©A is infinite. The class of P0-spaces contains all metrizable separable spaces and is (properly) contained in the Michael's class of âµ0-spaces. It is closed under many topological operations: taking subspaces, countable Tychonoff products, small countable box-products, countable direct limits, hyperspaces of compact subsets. For an âµ0-space X and a P0-space Y the function space Ck(X,Y) endowed with the compact-open topology is a P0-space. For any sequential âµ0-space X the free abelian topological group A(X) and the free locally convex linear topological space L(X) both are P0-spaces. A sequential space is a P0-space if and only if it is an âµ0-space. A topological space is metrizable and separable if and only if it is a P0-space with countable fan tightness.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Taras Banakh,