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.

Keywords: Metric space, $\pi$-mapping, pseudo-sequence-covering mapping, $wcs$-cover, $cs^*$-cover, point-star network.

MSC: 54E35, 54E40

Pages:  113$-$120     

Volume  57 ,  Issue  3$-$4 ,  2005