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


  • D. Singh University of Delhi
  • J.K. Kohli University of Delhi




R space, ultra Hausdorff space, initial property, monoreflective (epireflective) subcategory, R_cl-supercontinuous function, 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 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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Author Biography

D. Singh, University of Delhi

Deptt. of Mathematics

Asstt. Professor


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How to Cite

D. Singh and J. Kohli, “R-spaces and closedness/completeness of certain function spaces in the topology of uniform convergence”, Appl. Gen. Topol., vol. 15, no. 2, pp. 155–166, Aug. 2014.



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