A note on sequence-covering $\pi$-images of metric spaces

Zhaowen Li, Tusheng Xie

In this paper, we prove that a space is a sequence-covering $\pi$-image of a metric space if and only if it has a $\sigma$-strong network consisting of $cs$-covers (or $sn$-covers) if and only if it is a Cauchy $sn$-symmetric space.