Tag Archives: chain

Koch’s arc theorem

Posted on March 20, 2025 by jgl

Koch’s arc theorem is a famous theorem saying that, under a few conditions, given any point x of an open subset U of a pospace (X, ≤), one can draw an arc chain from some point on the boundary of … Continue reading →

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Arcs and arc chains

Posted on January 20, 2025 by jgl

Jimmie Lawson had presented some results about chains in partially ordered spaces at the ISDT conference in 2022, which I wanted to talk about. But this requires Koch’s arc theorem, so I decided to talk about the latter first. That … Continue reading →

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Chains and nested spaces

Posted on August 23, 2020 by jgl

A chain is a totally ordered poset, and a nested space is a topological space whose lattice of open sets is a chain. That may seem like a curious notion, although you might say that the Scott topology on the … Continue reading →

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