Rδ-Supercontinuous Functions

Abstract

A new class of functions called ‘Rδ-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 Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl- supercontinuous functions (Demonstratio Math. 46(1) (2013), 229-244) and so includes all Rcl-supercontinuous (≡clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293-300; Indian J. Pure Appl. Math. 14(6) (1983), 767-772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703-723).

Keywords

• z-supercontinuous function
• F-supercontinuous function
• cl-supercontinuous function
• Rz-supercontinuous function
• R-supercontinuous function
• rδ-open (rδ-closed)set
• δ-embedded
• weakly Hausdorff space (≡δT1-space)
• δT0-space