Every monovalued reloid is metamonovalued (Solved)

Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Topology
Keywords: monovalued
Recomm. for undergrads: no
Posted by: porton
on: September 17th, 2013
Solved by: Porton, Victor
Conjecture   Every monovalued reloid is metamonovalued.

Let $ f $ is a monovalued reloid. Then there is a principal filter $ X $ and principal monovalued reloid $ F $ such that $ f = F|_X $.

$ \left( \bigcap G \right) \circ f = \left( \bigcap G \right) \circ ( F|_X) = \left( \left( \bigcap G \right) \circ F \right) |_X $

It follows that it's enough to prove it for monovalued principal reloids.


Solved in the new version of this book preprint: *Algebraic General Toplogy. Volume 1

* indicates original appearance(s) of problem.