### ${R}_{z}$-supercontinuous functions

A new class of functions called “${R}_{z}$-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 ${R}_{z}$-supercontinuous functions properly includes the class of ${R}_{\mathrm{cl}}$-supercontinuous functions, Tyagi, Kohli, Singh (2013), which in its turn contains the class of $\mathrm{cl}$-supercontinuous ($\equiv $ clopen continuous) functions, Singh (2007), Reilly, Vamanamurthy (1983), and is...