Tag Archives: compact pospace

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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The fundamental theorem of compact semilattices

Posted on August 20, 2023 by jgl

Bounded-complete domains, or bc-domains, are an amazingly rich kind of continuous domains. They form a Cartesian-closed category, and they are the densely injective topological spaces, among other properties. One characterization of bc-domains which I have not included in the book … Continue reading →

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