Collections of compact sets and functions having \(G_\delta\)-graphs (Q2464601)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Collections of compact sets and functions having \(G_\delta\)-graphs |
scientific article |
Statements
Collections of compact sets and functions having \(G_\delta\)-graphs (English)
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2 January 2008
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The author investigates the connection between the structure of a function \(f\) defined on a subset of a space \(X\) and the Borel complexity of the set \(C(f)= \{C\in J(x): f|_C\) is continuous\}, where \(I(X)\) denotes the nonempty compact subsets of \(X\) with the Hausdorff metric. Two hierarchies of functions with \(G_\delta\)-graphs are also defined.
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Borel complexity
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continuous functions
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