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$$R_{\text{cl}}$$-supercontinuous functions. (English) Zbl 1272.54015
Summary: A new class of functions called ‘$$R_{\text{cl}}$$-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 $$R_{\text{cl}}$$-supercontinuous functions properly contains the class of cl-supercontinuous $$(\equiv$$ clopen continuous) functions D. Singh [Appl. Gen. Topol. 8, No. 2, 293–300 (2007; Zbl 1151.54012)]; I.L. Reilly and M.K. Vamanamurthy [Indian J. Pure Appl. Math. 14, 767–772 (1983; Zbl 0509.54007)] and is strictly contained in the class of $$R_\delta$$-supercontinuous functions which in its turn, is properly contained in the class of $$R$$-supercontinuous functions J.K. Kohli, D. Singh and J. Aggarwal [Demonstr. Math. 43, No. 3, 703–723 (2010; Zbl 1217.54016)].

##### MSC:
 54C08 Weak and generalized continuity 54C10 Special maps on topological spaces (open, closed, perfect, etc.) 54D10 Lower separation axioms ($$T_0$$–$$T_3$$, etc.) 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
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