Article ID Journal Published Year Pages File Type
4658422 Topology and its Applications 2015 13 Pages PDF
Abstract
In this paper, we investigate certain networks on free topological groups and free Abelian topological groups and obtain the following: (1) F(X) is a submetrizable, σ-space if and only if X is a submetrizable, σ-space; (2) Let X be a k⁎-metrizable, μ-space. F(X) is a k-space if and only if X is discrete or a k-space with a countable k-network consisting of compact subsets; A(X) is a k-space if and only if X is discrete or a k-space with a star-countable k-network consisting of compact subsets and the non-isolated point set is separable; (3) Suppose that X is a k⁎-metrizable, μ-space, then F4(X) is weakly first-countable if and only if X is discrete or compact; F(X) is a k-space if and only if F10(X) is a k-space.
Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
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