Abstract

In this paper, we give some characterizations of spaces with locally countable network and some characterizations of $sn$-symmetric (or Cauchy $sn$-symmetric) spaces with locally countable $sn$-networks by compact images (or $\pi$-images) of locally separable metric spaces.

Keywords: Network; $cs^*$-network; $sn$-network; weak base; locally countable; sequence-covering; $1$-sequence-covering; weak-open; compact map; $\pi$-map.

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

Pages:  84$-$90     

Volume  66 ,  Issue  1 ,  2014