In this paper a new generalization of $B^*$-continuity has been defined, to be called as $B^*$-clopen continuity and many of its properties have been studied including the convergence behaviour of sequences of such functions. Also a new type of oscillation function, called cl-oscillation has been defined, which characterizes the $B^*$-clopen continuity.
The second author is partially supported by DST grant no. SR/WOS-A/PM-106/2016 under the Women Scientists Scheme-A (WOS-A) and the third author is partially supported by UGC grant no. 20/12/2015(ii)EU-V.
The authors are thankful to Professor D. K. Ganguly for valuable inputs in the paper.
"On $B^*$-clopen continuity, oscillation and convergence." Tbilisi Math. J. 13 (4) 129 - 140, December 2020. https://doi.org/10.32513/tbilisi/1608606054