Compact-star networks and the images of metric spaces under C-mappings

Abstract

A sequence {Pn}n∈N of covers of a space X is called a compact-star network of X if for each open set U of X and each compact subset K⊂U, there is an n∈N such that st(K,Pn)⊂U. In this paper, cs-metrizable spaces and k-metrizable spaces are characterized by certain compact-star networks. Further, it is proved that metrizability is preserved by quotient and cs-regular mappings.