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Compact images of spaces with a weaker metric topology

Peng-fei Yan; Cheng Lü — 2008

Czechoslovak Mathematical Journal

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 ${ℱ_{i}}_{i \in ℕ}$ of point-finite $c s$ -covers such that $⋂_{i \in ℕ} st (y, ℱ_{i}) = {y}$ for each $y \in Y$ . (2) $Y$ is a sequentially-quotient...

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