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A funcoid related to directed topological spaces

Importance: Medium ✭✭
Author(s): Porton, Victor
Subject: Topology
Keywords:
Recomm. for undergrads: no
Posted by: porton
on: July 28th, 2016
Conjecture   Let $ R $ be the complete funcoid corresponding to the usual topology on extended real line $ [-\infty,+\infty] = \mathbb{R}\cup\{-\infty,+\infty\} $. Let $ \geq $ be the order on this set. Then $ R\sqcap^{\mathsf{FCD}}\mathord{\geq} $ is a complete funcoid.
Proposition   It is easy to prove that $ \langle R\sqcap^{\mathsf{FCD}}\mathord{\geq}\rangle \{x\} $ is the infinitely small right neighborhood filter of point $ x\in[-\infty,+\infty] $.

If proved true, the conjecture then can be generalized to a wider class of posets.

See Algebraic General Topology for definitions of used concepts.

Bibliography

* Blog post


* indicates original appearance(s) of problem.
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