On some spaces generated by \(\mu\)-regular sets (Q2788873)
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scientific article; zbMATH DE number 6544068
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some spaces generated by \(\mu\)-regular sets |
scientific article; zbMATH DE number 6544068 |
Statements
22 February 2016
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almost \(G\)-regular space
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\(\mu\)-semiregularization
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generalized topology
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\(G\)-semiregular space
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almost \((\mu,\mu')\)-continuous function
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super \((\mu,\mu')\)-continuous function
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\((\delta,\delta')\)-continuous function
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On some spaces generated by \(\mu\)-regular sets (English)
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A generalized topological space \((X,\mu)\) is said to be almost \(G\)-regular if for each \(x\in\Lambda_\mu\) (where \(\Lambda_\mu\) is the union of all \(\mu\)-open sets in \((X,\mu)\)) and each \(\mu\)-regular closed \(F\) with \(x\notin F\) there are disjoint \(\mu\)-open sets \(U\) and \(V\) such that \(x\in U\) and \(F\cap\Lambda_{\mu}\subset V\). A space is said to be \(G\)-semiregular if it is generated by \(\mu\)-regular open sets. Some properties of such spaces are investigated.
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