Gao, Zhimin \(\aleph\)-space is invariant under perfect mappings. (English) Zbl 0636.54026 Quest. Answers Gen. Topology 5, 271-279 (1987). 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. Cited in 2 ReviewsCited in 28 Documents MSC: 54E20 Stratifiable spaces, cosmic spaces, etc. 54C10 Special maps on topological spaces (open, closed, perfect, etc.) Keywords:\(\aleph \)-space; perfect mappings; K-semi-stratifiable spaces; closed mappings PDFBibTeX XMLCite \textit{Z. Gao}, Quest. Answers Gen. Topology 5, 271--279 (1987; Zbl 0636.54026)