The aim of this paper is to introduce and characterize the vividly (1,2)-$\beta$-irresolute mapping and blurly (1,2)-$\beta$-irresolute mapping. We also define (1,2)-$\beta$-$T_2$ spaces and (1,2)-semi-preregular spaces. These spaces are characterized by a new class of open sets, called (1,2)-semipre-$\theta$-open sets.