Continuous functions with compact support
The main aim of this paper is to investigate a subring of the ring of continuous functions on a topological space X with values in a linearly ordered field F equipped with its order topology, namely the ring of continuous functions with compact support. Unless X is compact, these rings are commutati...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2004-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1999 |
| Summary: | The main aim of this paper is to investigate a subring of the ring of continuous functions on a topological space X with values in a linearly ordered field F equipped with its order topology, namely the ring of continuous functions with compact support. Unless X is compact, these rings are commutative rings without unity. However, unlike many other commutative rings without unity, these rings turn out to have some nice properties, essentially in determining the property of X being locally compact non-compact or the property of X being nowhere locally compact. Also, one can associate with these rings a topological space resembling the structure space of a commutative ring with unity, such that the classical Banach Stone Theorem can be generalized to the case when the range field is that of the reals. |
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| ISSN: | 1576-9402 1989-4147 |