A new characterization of spaces with locally countable $sn$-networks

摘要

In this paper we prove that a space X is with a locally countable sn-network (re- sp., weak base) if and only if it is a compact-covering (resp., compact-covering quotient) compact and ss-image of a metric space, if and only if it is a sequentially-quotient (resp., quotient) π- and ss-image of a metric space, which gives a new characterization of spaces with locally countable sn-networks (or weak bases).