On weak structures and \(w\)-spaces (Q2796443)
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scientific article; zbMATH DE number 6560214
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On weak structures and \(w\)-spaces |
scientific article; zbMATH DE number 6560214 |
Statements
24 March 2016
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WNS
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weak structure
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\(w\)-spaces
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\(W\)-continuous
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\(W^*\)-continuous
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\(W\)-compact
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On weak structures and \(w\)-spaces (English)
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For a nonempty set \(X\), a family \(w_X\) of subsets of \(X\) is called a weak structure on \(X\) if \ \(\emptyset , X \in w_X\) \ and \ \(U_1,U_2 \in w_X \;\Rightarrow \;U_1\cap U_2 \in w_X\) . The pair \ \((X,w_X)\) \ is called a \(w\)-space on \(X\), and the elements of \(w_X\) are called \(w\)-open (and their complements \(w\)-closed).NEWLINENEWLINEThe authors study corresponding notions of interior, closure and continuity in a rather elementary fashion.
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