On some low separation axioms via \(\lambda\)-open and \(\lambda\)-closure operator (Q861986)
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scientific article; zbMATH DE number 5121514
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some low separation axioms via \(\lambda\)-open and \(\lambda\)-closure operator |
scientific article; zbMATH DE number 5121514 |
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On some low separation axioms via \(\lambda\)-open and \(\lambda\)-closure operator (English)
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2 February 2007
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A subset of a topological space is called a \(\lambda\)-closed set, if it is an intersection of a closed set and of an intersection of open sets. Using this kind of closedness, the separation axioms \(R_0\) and \(R_1\) are modified to \(\lambda\)-\(R_0\) and \(\lambda\)-\(R_1\). Thus, e.g., \(X\) is a \(\lambda\)-\(R_0\)-space if every \(\lambda\)-open set contains a \(\lambda\)-closure of each of its points. Basic properties and relations for those new separations are studied.
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Topological spaces
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\(\lambda\)-open sets
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\(\lambda\)-closure
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\(\lambda\)-\(R_0\) and \(\lambda\)-\(R_1\)
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