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Rcl-supercontinuous functions

Tyagi B. K., Kohli J. K., Singh D.

Demonstratio Mathematica

2013

Vol. 46, nr 1

229--244

A new class of functions called ‘Rcl-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. The class of Rcl-supercontinuous functions properly contains the class of cl-supercontinuous (≡ clopen continuous) functions (Applied Gen. Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is strictly contained in the class of Rδ-supercontinuous functions which in its turn, is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).