A NOTE ON WEAKLY IRRESOLUTE MAPPINGS

A mapping f: X$\rightarrow$Y is introduced to be weakly irresolute if, for each x $\varepsilon$ X and each semi-neighborhood V of f(x), there exists a semi-neighborhood U of x in X such that $f(U){\subset}scl(V)$. It will be shown that a mapping f: X$\rightarrow$Y is weakly irresolute iff(if and only if) $f^{-1}(V){\subset}sint(f^{_1}(scl(V)))$ for each semiopen subset V of Y. The relationship between mappings described in [3,5, 6,8] and a weakly irresolute mapping. will be investigated and it will be shown that every irresolute retract of a $T_2$-space is semiclosed.