R-supercontinuous functions

• Autorzy: Kohli J. K. , Singh D. , Aggarwal J.
• Języki publikacji: EN

Abstrakty

EN

A new strong variant of continuity called 'R-supercontinuity' is introduced. Basic properties of R-supercontinuous functions are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. It is shown that R-supercontinuity is preserved under the restriction, shrinking and expansion of range, composition of functions, products and the passage to graph function. The class of R-supercontinuous functions properly contains each of the classes of (i) strongly (...)-continuous functions introduced by Noiri and also studied by Long and Herrington; (ii) D-supercontinuous functions; and (iii) F-supercontinuous functions; and so include all z-supercontinuous functions and hence all clopen maps ((...) cl-supercontinuous functions) introduced by Reilly and Vamnamurthy, perfectly continuous functions defined by Noiri and strongly continuous functions due to Levine. Moreover, the notion of r-quotient topology is introduced and its interrelations with the usual quotient topology and other variants of quotient topology in the literature are discussed. Retopologization of the domain of a function satisfying a strong variant of continuity is considered and interrelations among various coarser topologies so obtained are observed.

Słowa kluczowe

EN

strongly (theta)-continuous function; supercontinuous function; D-supercontinuous function; F-supercontinuous function; R0-space; r-quotient topology; (delta)-quotient topology; (theta)-quotient topology; r-open set

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 3
• Strony: 703--723
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Kohli J. K.

autor

Singh D.

autor

Aggarwal J.

• Department of Mathematics Hindu College University of Delhi, Delhi 110007, India,

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