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Closed maps on spaces with point-countable bases

✍ Scribed by Alexander Shibakov

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 134 KB
Volume: 96
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(98)00013-3

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✦ Synopsis

We prove a version of Lašnev's theorem for spaces with point-countable bases.

Then we study the subspaces of closed images of regular spaces with point-countable bases and show that every such subspace has countable π-character and a point-countable π-base. The latter result is extended to a wider class of spaces which is invariant under closed maps and products with metrizable compacta. The proofs use a structure which controls the convergence properties of the space and those of its closed image.

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