Regularity and extension of maps. (English) Zbl 0762.54019

Regular topological spaces \(Y\) are known to be characterized by the property that a mapping \(f:X\to Y\) is continuous provided, for a given dense set \(X_ 0\) of \(X\), its restriction to every subspace \(X_ 0\cup \{x\}\) is continuous. The authors show that this characterization is also true for convergence spaces if one uses strict dense sets \(X_ 0\) only. This description is then used to define regularity in \(\mathcal L\)-spaces; an inner characterization of such regular \(\mathcal L\)-spaces is given.
Reviewer: M.Hušek (Praha)


54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54C20 Extension of maps
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