I’ve found a counterexample to the following conjecture:
Statement For every composable funcoids and we have
The counterexample is and , where is an arbitrary nontrivial ultrafilter and is an arbitrary point.
I leave the proof that it is a counterexample as an easy exercise for the reader (however I am going to add the proof to my book soon).
That the conjecture failed invalidates my new proof of Urysohn’s lemma which was based on this conjecture.