I started research of mappings between endofuncoids and topological spaces.

Currently the draft is located in volume 2 draft of my online book.

I define mappings back and forth between endofuncoids and topologies.

The main result is a representation of an endofuncoid induced by a topological space.

The formula is $latex f\mapsto 1\sqcup\mathrm{Compl}\, f\sqcup(\mathrm{Compl}\, f)^2\sqcup \dots$.

However I proved this theorem only for the special case if every singleton is a closed set. Also the proof is not yet checked for errors.

The proof was with a fatal error. I have removed the said theorem from my drafts. Instead I’ve added a counterexample.