A Class Of Mappings Between R-Z-Supercontinuous Functions And R-Delta-Supercontinuous Functions
HONAM MATHEMATICAL JOURNAL(2017)
Abstract
A new class of functions called R-theta-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of R-theta-supercontinuous functions properly contains the class of R-z-supercontinuous functions [39] which in turn properly contains the class of R-cl-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of R-delta-supercontinuous functions [24].
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Key words
theta-open (closed) set, r(theta)-open (closed) set, R-1-space, theta-embeded, r(theta)-quotient map, R-theta-open (closed) map, P-regular space, completely P-regular space, change of topology, P-continuous functions, P*-continuous functions
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