
uniformity
Direct proof of a theorem about compact funcoids ★★
Author(s): Porton
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


Then .
Keywords: compact space; compact topology; funcoid; reloid; uniform space; uniformity
