R-spaces and closedness/completeness of certain function spaces in the topology of uniform convergence
It is shown that the notion of an − cl R space (Demonstratio Math. 46(1) (2013), 229-244) fits well as a separation axiom between zero dimensionality and − 0 R spaces. Basic properties of − cl R spaces are studied and their place in the hierarchy of separation axioms that already exist in the litera...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2014-08-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/3029 |
| Summary: | It is shown that the notion of an − cl R space (Demonstratio Math. 46(1) (2013), 229-244) fits well as a separation axiom between zero dimensionality and − 0 R spaces. Basic properties of − cl R spaces are studied and their place in the hierarchy of separation axioms that already exist in the literature is elaborated. The category of − cl R spaces and continuous maps constitutes a full isomorphism closed, monoreflective (epireflective) subcategory of TOP. The function space cl R (X, Y) of all − cl R supercontinuous functions from a space X into a uniform space Y is shown to be closed in the topology of uniform convergence. This strengthens and extends certain results in the literature (Demonstratio Math. 45(4) (2012), 947-952). |
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| ISSN: | 1576-9402 1989-4147 |