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Decomposition of completions of reloids

Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Topology
Keywords: co-completion
completion
reloid
Recomm. for undergrads: no
Posted by: porton
on: September 2nd, 2013
Conjecture   For composable reloids $ f $ and $ g $ it holds
    \item $ \operatorname{Compl} ( g \circ f) = ( \operatorname{Compl} g) \circ f $ if $ f $ is a co-complete reloid; \item $ \operatorname{CoCompl} ( f \circ g) = f \circ \operatorname{CoCompl} g $ if $ f $ is a complete reloid; \item $ \operatorname{CoCompl} ( ( \operatorname{Compl} g) \circ f) = \operatorname{Compl} ( g \circ ( \operatorname{CoCompl} f)) = ( \operatorname{Compl} g) \circ ( \operatorname{CoCompl} f) $; \item $ \operatorname{Compl} ( g \circ ( \operatorname{Compl} f)) = \operatorname{Compl} ( g \circ f) $; \item $ \operatorname{CoCompl} ( ( \operatorname{CoCompl} g) \circ f) = \operatorname{CoCompl} ( g \circ f) $.

Well, in fact this is three separate problems (if we count dual formulas as one formula), but I am lazy to create three pages for them.

This conjecture is inspired by the proven fact that the above formulas hold for every composable funcoids $ f $ and $ g $ (instead of reloids). Properties of reloids are expected to be similar to properties of funcoids.

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Bibliography

*Algebraic General Toplogy. Volume 1


* indicates original appearance(s) of problem.
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