Jinjin Li, Zhaowen Li

A Positive Answer to Velichko's Question

We give positive answer to Velichko's question in which the quotient and $s$-map is replaced by a sequence-covering and $cs$-map. In addition, let $X$ have a star-countable $k$-network, then $X$ is a sequence-covering and $cs$-image of a locally separable metric space if and only if $X$ is a sequence-covering and $cs$-image of a metric space.

Sequence-covering maps, $cs$-mappings, cs-networks, $k$-networks, compact-countable covers, star-countable collections, cosmic spaces, $\aleph_{0}$-spaces.

MSC 2000: Primary 54E99, 54C10. Secondary 54D55