Pointwise Products of Uniformly Continuous Functions
The problem of characterizing the metric spaces on which the pointwise product of any two uniformly continuous real - valued functions is uniformly continuous is investigated. A sufficient condition is given; furthermore, the condition is shown to be necessary for certain types of metric spaces, whi...
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| Published in | Sarajevo journal of mathematics Vol. 1; no. 1; pp. 117 - 127 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
12.06.2024
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| Online Access | Get full text |
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| Summary: | The problem of characterizing the metric spaces on which the pointwise product of any two uniformly continuous real - valued functions is uniformly continuous is investigated. A sufficient condition is given; furthermore, the condition is shown to be necessary for certain types of metric spaces, which include those with no isolated point and all subspaces of Euclidean spaces. It is not known if the condition is always necessary.
2000 Mathematics Subject Classification. Primary: 54C10, 54C30; Secondary: 20M20 |
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| ISSN: | 1840-0655 2233-1964 |
| DOI: | 10.5644/SJM.01.1.10 |