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The inverse images of hyperconnected sets. (English) Zbl 0607.54016

The authors prove two results: (1) the \(\alpha\)-continuous image of a semi-open hyperconnected set is hyperconnected, (2) preopen hyperconnected sets are inverse preserved under semi-closed preserving surjections with preopen hyperconnected point inverses. Recall that a topological space X is said to be hyperconnected if each non-empty open set in X is dense in X, and that a subset of X is said to be a hyperconnected set if it is hyperconnected as a subspace.
Reviewer: I.L.Reilly

MSC:

54D05 Connected and locally connected spaces (general aspects)
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