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A note on sequence-covering mappings. (English) Zbl 1081.54025

Summary: Let \(f : X \to Y\) be a mapping. \(f\) is called a sequence-covering mapping if in case \(S\) is a convergent sequence containing its limit point in \(Y\) then there is a compact subset \(K\) of \(X\) such that \(f(K) = S\). It is shown that each quotient and compact mapping of a metric space is sequence-covering.

MSC:

54E40 Special maps on metric spaces
54E20 Stratifiable spaces, cosmic spaces, etc.
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
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