Products of straight spaces with compact spaces
| Autor: | Kusuo Nishijima, Kohzo Yamada |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Applied General Topology, Vol 8, Iss 2, Pp 151-159 (2007) |
| Druh dokumentu: | article |
| ISSN: | 1576-9402 1989-4147 |
| DOI: | 10.4995/agt.2007.1877 |
| Popis: | A metric space X is called straight if any continuous real-valued function which is uniformly continuous on each set of a finite cover of X by closed sets, is itself uniformly continuous. Let C be the convergent sequence {1/n : n ϵ N} with its limit 0 in the real line with the usual metric. In this paper, we show that for a straight space X, X × C is straight if and only if X × K is straight for any compact metric space K. Furthermore, we show that for a straight space X, if X × C is straight, then X is precompact. Note that the notion of straightness depends on the metric on X. Indeed, since the real line R with the usual metric is not precompact, R×C is not straight. On the other hand, we show that the product space of an open interval and C is straight. |
| Databáze: | Directory of Open Access Journals |
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