**Jinjin Li, Zhaowen Li**

## A Positive Answer to Velichko's
Question

**Abstract:**

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.

**Keywords:**

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