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.
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Supported by the NNSF(10471084) of China.
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Yan, Pf., Lü, C. Compact images of spaces with a weaker metric topology. Czech Math J 58, 921–926 (2008). https://doi.org/10.1007/s10587-008-0060-5
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DOI: https://doi.org/10.1007/s10587-008-0060-5