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July 28, 2016 / porton

A funcoid related to directed topological spaces

The following problem arose from my attempt to re-express directed topological spaces in terms of funcoids.

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.

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