On pseudo-sequence coverings, $\pi$-images of metric spaces

Ying Ge

Abstract

In this paper, we prove that a space $X$ is a pseudo-sequence-covering,
$\pi$-image of a metric space if and only if $X$ has a point-star network consisting of
$wcs$-covers, which answers a conjecture posed by Lin affirmatively.
As an application of this result, we have that a space is
a pseudo-sequence-covering, $\pi$-image of a separable metric space
is characterized as a sequentially-quotient, $\pi$-image of a separable metric space.