R-spaces and closedness/completeness of certain function spaces in the 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 litera...

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Bibliographic Details
Published in:	Applied general topology Vol. 15; no. 2; pp. 155 - 166
Main Authors:	Singh, Davinder, Kohli, J. K.
Format:	Journal Article
Language:	English
Published:	Universitat Politècnica de València 04.08.2014
Subjects:	initial property monoreflective (epireflective) subcategory R space R_cl-supercontinuous function topology of uniform convergence ultra Hausdorff space
ISSN:	1576-9402, 1989-4147
Online Access:	Get full text
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Summary:	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).
ISSN:	1576-9402 1989-4147
DOI:	10.4995/agt.2014.3029