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R-spaces and closedness/completeness of certain function spaces in the topology of uniform convergence

  • Singh, Davinder [1] ; Kohli, J. K. [1]
    1. [1] University of Delhi

      University of Delhi

      India

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 15, Nº. 2, 2014, págs. 155-166
  • Idioma: inglés
  • DOI: 10.4995/agt.2014.3029
  • Enlaces
  • Resumen

    • 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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