Advanced Search

If $X$ is a space that can be mapped onto a metric space by a one-to-one mapping, then $X$ is said to have a weaker metric topology. In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces with a weaker metric topology. The main results are that (1) $Y$ is a sequence-covering compact image of a space with a weaker metric topology if and only if $Y$ has a sequence ${\left\{{ℱ}_i\right\}}_{i\in \mathbb{N}}$ of point-finite $cs$-covers such that ${\bigcap }_{i\in \mathbb{N}}\mathrm{st}(y,{ℱ}_i)=\left\{y\right\}$ for each $y\in Y$. (2) $Y$ is a sequentially-quotient...