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

D. Singh, J.K. Kohli

Abstract

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).

Keywords

R space; ultra Hausdorff space; initial property; monoreflective (epireflective) subcategory; R_cl-supercontinuous function; topology of uniform convergence

Subject classification

54C08; 54C10; 54C35; 54D05; 54D10

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