Absolute weak $C$-embedding in Hausdorff spaces (Problems and applications in General and Geometric Topology)

Answering aproblem of A. V. $\mathrm{A}\mathrm{r}\mathrm{h}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{e}1' \mathrm{s}\mathrm{k}\mathrm{i}_{\dot{1}}$ , we give acharacter- ization of absolute weak $C$ -embedding in Hausdorff spaces.We also introduce an alternative proof of the Bella-Yaschenko Theorem, which characterize absolute weak $C$ -embedding in Tychonoff spaces.