On spaces with point-star networks consisting of cs-finite cs⁎-coverings

Abstract

In this paper, by a finite-type property P, some characterizations of point-star networks consisting of P and cs⁎-coverings are discussed in Cauchy sn-symmetric spaces. Then it is established that the relations between spaces with point-star networks consisting of certain cs⁎-coverings and the images of metric spaces under some mappings, which extends and unifies some results of An and Tuyen in 2018, and gives a partial answer to the following question posed by Tanaka and Ge in 2006: Is a symmetric space having a σ-point-finite cs⁎-network a quotient compact image of a metric space?