On spaces with aG?-basis

Brandenburg, Harald

doi:10.1007/bf01235379

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…The space X is a functionally regular space, since it is a functionally Hausdorff Lindelöf space (see [1,Theorem 3]). The space X is not D-regular, since X is not a subparacompact space and every Lindelöf, D-regular space is subparacompact (see [4,Theorem 2]). Then the identity mapping defined on X is an F -supercontinuous function but not a D-supercontinuous function.…”

Section: 3mentioning

confidence: 99%

F-supercontinuous functions

2009

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A strong variant of continuity called 'F -supercontinuity' is introduced. The class of F -supercontinuous functions strictly contains the class of z-supercontinuous functions (Indian J. Pure Appl. Math. 33 (7) (2002), 1097-1108) which in turn properly contains the class of cl-supercontinuous functions (≡ clopen maps) (Appl. Gen. Topology 8 (2) (2007), 293-300; Indian J. Pure Appl. Math. 14 (6) (1983), 762-772). Further, the class of F -supercontinuous functions is properly contained in the class of R-supercontinuous functions which in turn is strictly contained in the class of continuous functions. Basic properties of F -supercontinuous functions are studied and their place in the hierarchy of strong variants of continuity, which already exist in the mathematical literature, is elaborated. If either domain or range is a functionally regular space (

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Section: 3mentioning

confidence: 99%

F-supercontinuous functions

2009

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“…A family T of closed sets in X is called a strongly closed Gs-family [3] if each F 6 T is the countable intersection F = f){X -F{ \ Fi 6 F}\ the members of any such family T are called strongly closed Gs-sets [3]. It turns out that strongly closed Gs-sets are precisely the Z?-closed sets [13].…”

Section: Basic Definitions and Preliminariesmentioning

confidence: 99%

A unified approach to continuous and certain non-continuous functions II

Kohli

1990

Bull. Austral. Math. Soc.

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A unified theory of continuous and certain non-continuous functions, initiated in an earlier paper, is further elaborated. The proposed theory provides a common platform for dealing simultaneously with continuous functions and a host of non-continuous functions including lower (upper) semicontinuous functions, almost continuous functions, weakly continuous functions (encountered in functional analysis), c-continuous functions, S-continuous functions, semiconnected functions, iif-continuous functions s-continuous functions, e-continuous functions of Klee and several other variants of continuity.

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