Compact images of spaces with a weaker metric topology |
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Authors: | Peng-fei Yan Cheng Lü |
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Institution: | (1) Department of Mathematics and Physics, Wuyi University, Guangdong, 529 020, China;(2) Department of Mathematics and Physics, Anhui Institute of Architecture and Industry, Anhui, 230 022, China |
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Abstract: | 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
of point-finite cs-covers such that
for each y ∈ Y.
(2) Y is a sequentially-quotient compact image of a space with a weaker metric topology if and only if Y has a sequence
of point-finite cs*-covers such that
for each y ∈ Y.
Supported by the NNSF(10471084) of China. |
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Keywords: | sequence-covering mappings sequentially-quotient mappings compact mappings weaker metric topology |
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