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On Hausdorff spaces via ideals and quasi \(I\)-irresolute functions. (English) Zbl 1010.54022

The author considers the notion of quasi-\(I\)-open sets in a topological space \(X\) (where \(I\) denotes an ideal on \(X\)). Using this notion two new concepts are introduced and investigated, namely quasi-\(I\)-Hausdorffness as a separation axiom, and quasi-\(I\)-irresoluteness as a property of functions between topological spaces both of which are endowed with an ideal.

MSC:

54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54C08 Weak and generalized continuity
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