Direct proof of a theorem about compact funcoids

porton — Sat, 08 Feb 2014 15:51:03 +0100

Author(s): Porton

Subject: Topology

Conjecture Let is a -separable (the same as for symmetric transitive) compact funcoid and is a uniform space (reflexive, symmetric, and transitive endoreloid) such that . Then .

The main purpose here is to find a direct proof of this conjecture. It seems that this conjecture can be derived from the well known theorem about existence of exactly one uniformity on a compact set. But that would be what I call an indirect proof, we need a direct proof instead.

The direct proof may be constructed by correcting all errors an omissions in this draft article.

Direct proof could be better because with it we would get a little more general statement like this:

Conjecture Let be a -separable compact reflexive symmetric funcoid and be a reloid such that

\item ; \item .

Then .

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Direct proof of a theorem about compact funcoids