The bounded-open topology and its relatives (Q2785353)
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scientific article; zbMATH DE number 980861
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The bounded-open topology and its relatives |
scientific article; zbMATH DE number 980861 |
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20 February 1997
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uniform topology on bounded sets
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0.89689696
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0.89624643
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The bounded-open topology and its relatives (English)
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The authors study two collections of topologies on the set \(C(X)\) of continuous real-valued functions on \(X\): the set-open topologies and the uniform topologies, both over certain families of bounded sets in \(X\) (including the families of all finite sets, compact sets, countably compact sets, pseudocompact sets, and bounded sets). A detailed comparison of these topologies is made, and a number of examples are given. Also the properties of separable, metrizable, and complete are characterized for the uniform topologies in general.
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