Abstract

In this paper we prove that a space $X$ is with a locally countable $sn$-network (resp., 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) $\pi$- and $ss$-image of a metric space, which gives a new characterization of spaces with locally countable $sn$-networks (or weak bases).

Keywords: Weak base; $sn$-network; $\sigma$-strong network; locally countable; compact-covering; compact map; $\pi$-map.

MSC: 54C10, 54D65, 54E40, 54E99

Pages:  8$-$13     

Volume  65 ,  Issue  1 ,  2013