Three-space properties of some kinds of coset spaces

Abstract

In this paper, some three-space properties of (compactly-fibered, neutrally-fibered) coset spaces are considered. Let X=G/H be a coset space and K a closed subgroup of G with H⊂K. It is mainly shown that (1) If G/H is neutrally-fibered, then G/H is second-countable ⇔ K/H and G/K are second-countable; (2) If G/H is compactly-fibered such that all compact (resp., countably compact) subspaces of K/H and G/K are metrizable, then all compact (resp., countably compact) subspaces of G/H are metrizable; (3) If G/H is neutrally-fibered such that K/H is second-countable and G/K an ℵ0-space (resp., cosmic), then G/H is an ℵ0-space (resp., cosmic); (4) If G/H is neutrally-fibered such that K/H is second-countable and G/K has a star-countable cs-network, then G/H has a star-countable cs-network; (5) If G/H is compactly-fibered such that K/H is locally compact metrizable and G/K stratifiable (resp., k-semi-stratifiable), then G/H is stratifiable (resp., k-semi-stratifiable).