Continuous functions with compact support

• Acharyya, S.K. ^[1] ; Chattopadhyaya, K.C. ^[2] ; Ghosh, Partha Pratim ^[3]
  1. [1] University of Calcutta

     University of Calcutta

     India

     
  2. [2] University of Burdwan

     University of Burdwan

     India

     
  3. [3] University of Cape Town

     University of Cape Town

     City of Cape Town, Sudáfrica

     

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• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 5, Nº. 1, 2004, págs. 103-113
• Idioma: inglés
• DOI: 10.4995/agt.2004.1999
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• Resumen

  • 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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