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Inner reloid through the lattice Gamma (Solved)

Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Topology
Keywords: filters
funcoids
inner reloid
reloids
Recomm. for undergrads: no
Posted by: porton
on: September 25th, 2014
Solved by: Porton, Victor
Conjecture   $ (\mathsf{RLD})_{\operatorname{in}} f = \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $ for every funcoid $ f $.

Counter-example: $ (\mathsf{RLD})_{\operatorname{in}} f \sqsubset \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f $ for the funcoid $ f = (=)|_\mathbb{R} $ is proved 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

* blog post


* indicates original appearance(s) of problem.
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