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Keywords:
$z$-supercontinuous function; $F$-supercontinuous function; $\rm cl$-supercontinuous function; $R_z$-supercontinuous function; $R$-supercontinuous function; $r_z$-open set; $r_z$-closed set; $z$-embedded set; $R_z$-space; functionally Hausdorff space
$z$-supercontinuous function; $F$-supercontinuous function; $\rm cl$-supercontinuous function; $R_z$-supercontinuous function; $R$-supercontinuous function; $r_z$-open set; $r_z$-closed set; $z$-embedded set; $R_z$-space; functionally Hausdorff space
Summary:
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 $R_{\rm cl}$-supercontinuous functions, Tyagi, Kohli, Singh (2013), which in its turn contains the class of $\rm cl$-supercontinuous ($\equiv $ clopen continuous) functions, Singh (2007), Reilly, Vamanamurthy (1983), and is strictly contained in the class of $R_{\delta }$-supercontinuous, Kohli, Tyagi, Singh, Aggarwal (2014), which in its turn is properly contained in the class of $R$-supercontinuous functions, Kohli, Singh, Aggarwal (2010).
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