# gn.general topology – Is the Cantor set zero-dimensional base?

Definition. A topological space of zero dimension. $$X$$ is called zero-dimensional basis yes for any base $$mathcal B$$ of the topology that consists of closed and open sets in $$X$$, any lid open $$mathcal U$$ of $$X$$ has a disjointed refinement $$mathcal V subset mathcal B$$.

It can be shown that each regular accounting space is a zero-dimensional basis.

Issue. It's the singer's cube $${0,1 } ^ omega$$ zero-dimensional basis?