On separation axioms of uniform bundles and sheaves

Neira U., Clara M. ^[1] ; Varela, Januario ^[1]
1. [1] Universidad Nacional de Colombia
  
  Universidad Nacional de Colombia
  
  Colombia
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 5, Nº. 2, 2004, págs. 155-171
Idioma: inglés
DOI: 10.4995/agt.2004.1966
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Resumen
- In the context of the theory of uniform bundles in the sense of J. Dauns and K. H. Hofmann, the topology of the fiber space of a uniform bundle depends on the assumption of upper semicontinuity of its defining set of pseudometrics when composed with local sections. In this paper we show that the additional hypothesis of lower semicontinuity of these functions secures that the fiber space of the uniform bundle is Hausdorff, regular or completely regular provided that the base space has the corresponding separation axiom. Similar results for the particular important case of sheaves of sets follow suit.
Referencias bibliográficas
- J. Dauns, K. H. Hofmann, Representations of rings by sections, Mem. Amer. Math. Soc. 83 (1968).
- F. B. Jones, Concerning normal and completely normal spaces, Bull. Amer. Math. Soc. 43 (1937) 671-677. http://dx.doi.org/10.1090/S0002-9904-1937-06622-5
- J. L. Kelley, General Topology, D. Van Nostrand Company, Inc. , (Canada, 1955).
- J. Varela, Existence of Uniform Bundles, Rev. Colombiana Mat. 18 (1984) 1-8.
- S. Willard, General Topology, Addison Wesley, (1970).