Comparisons of some weak forms of continuity (Q2460684)

This paper belongs to the category of examinations of relations between various more and more refined notions of weakened continuity and corresponding generalized open sets. In this case \(A\)-continuity and \(B\)-continuity of Tong and several weak forms of continuity introduced by \textit{T. H. Yalvaç} [Math. Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 19, No. 2, 177--183 (1990; Zbl 0729.54005)] and \textit{G. Aslim} and \textit{Y. Ayhan} [Acta Math. Hung. 105, No. 1-2, 85--91 (2004; Zbl 1059.54014)] are compared, and consequences of the definitions are extracted.