On cleavability over \(T_{i,\rho}\) spaces (Q1373420)
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scientific article; zbMATH DE number 1089790
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On cleavability over \(T_{i,\rho}\) spaces |
scientific article; zbMATH DE number 1089790 |
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On cleavability over \(T_{i,\rho}\) spaces (English)
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22 February 1998
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Let \(\mathcal P\) be a class of topological spaces and \(\mathcal M\) a class of continuous mappings. A space \(X\) is \(\mathcal M\)-cleavable over \(\mathcal P\) if for every \(A \subset X\) there are a space \(Y \in \mathcal P\) and a mapping \(f\in \mathcal M\) from \(X\) into \(Y\) such that \(f^{\gets}f(A) = A\). A natural question is: if a space \(X\) is \(\mathcal M\)-cleavable over \(\mathcal P\), does \(X\) belong to \(\mathcal P\)? The authors consider this question in connection with some separation axioms.
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cleavability over a class
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double cleavability
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pointwise cleavability
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\(T_{i,\rho}\) space
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