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Funcoid corresponding to reloid through lattice Gamma (Solved)

Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Topology
Keywords: funcoid corresponding to reloid
Recomm. for undergrads: no
Posted by: porton
on: September 26th, 2014
Solved by: Porton, Victor
Conjecture   For every reloid $ f $ and $ \mathcal{X} \in \mathfrak{F} (\operatorname{Src} f) $, $ \mathcal{Y} \in \mathfrak{F} (\operatorname{Dst} f) $:
    \item $ \mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y} \Leftrightarrow \forall F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f : \mathcal{X} \mathrel{[F]} \mathcal{Y} $; \item $ \langle (\mathsf{FCD}) f \rangle \mathcal{X} = \bigcap_{F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f} \langle F \rangle \mathcal{X} $.

It's proved by me in this online article.

It's used notation from Algebraic General Topology draft book, modified by this note about new notation for a future version of this book.

Bibliography



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