Extending monomorphic functors with finite supports

Анотація

We prove that each monomorphic functor with finite supports $F:Comp\to Comp$ has a unique extension $\overline{F}:TYCH\to TYCH$ to the category $TYCH$ of Tychonoff spaces and their arbitrary maps such that $\overline{F}|Tych=F_{\beta }$ where $F_{\beta }:Tych\to Tych$ is the extension of the functor $F$ to the category $Tych$ of Tychonoff spaces and their continuous maps, constructed by Chigogidze.