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\(\aleph\)-space is invariant under perfect mappings. (English) Zbl 0636.54026

Summary: We prove that if X is an \(\aleph\)-space and \(f: X\to Y\) closed map, with \(\partial f^{-1}(y)\) Lindelöf for each \(y\in Y\), then Y is an \(\aleph\)-space. This answers a question of Y. Tanaka. As a corollary of the main result, we have that \(\aleph\)-spaces are invariant under perfect mappings and K-semi-stratifiable spaces are invariant under closed mappings.

MSC:

54E20 Stratifiable spaces, cosmic spaces, etc.
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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