Density-to-deep-\(\mathcal I\)-density continuous functions (Q1189083)
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scientific article; zbMATH DE number 54502
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Density-to-deep-\(\mathcal I\)-density continuous functions |
scientific article; zbMATH DE number 54502 |
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Density-to-deep-\(\mathcal I\)-density continuous functions (English)
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26 September 1992
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The aim of the paper is to prove that the class of all real functions of a real variable which are continuous with respect to the deep \(I\)-density topology on the range and the density topology on the domain consists only of constant functions. The proof is by no means trivial and uses subtle properties of both topologies under consideration as well as special classes of functions like Baire*1 functions.
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continuous functions
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deep \(I\)-density topology
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Baire*1 functions
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range
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