Georgian Mathematical Journal 13 (2006), No. 2, 291--296
Copyright Heldermann Verlag 2006
A Positive Answer to Velichko's Question
Jinjin Li
Dept. of Mathematics, Zhangzhou Teachers' College, Zhangzhou, Fujian 363000, P. R. China
jinjinli@fjzs.edu.c
Zhaowen Li
Dept. of Mathematics, Changsha University of Electric Power, Changsha, Hunan 410077, P. R. China
We give a 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: 54E99, 54C10; 54D55
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