Abstract
In this work, some new connotations of continuous mappings such as $alpha^{*}$ - continuous mapping $left(alpha^{*}-C Mright),$ irresolute $alpha^{*}-$mapping $left(I alpha^{*}-C Mright),$ and strongly $alpha^{*}-$ continuous mapping $left(S alpha^{*}-C Mright)$ are studied and some of their characteristics are discussed. In other side, new some classes of contra continuous mappings are investigated in this work, they are called contra $alpha^{*}$ - continuous mapping $left(C alpha^{*}-C Mright)$.
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