Topologies defined on partially-ordered sets

Chris Tedd

G.209,

There are many ways in which one may define a topology from an ordering on a set, some familiar, some less so. In this talk we concentrate on such topologies that are "compatible" with the order relation in a certain sense, and see how purely order-theoretic properties of a poset can be translated into topological properties of the spaces so defined. In particular, an order-compatible topology on a poset is _spectral_ (cf. pure postgrads, passim) if and only if the poset in question is the inclusion ordering on the prime ideals of some ring.

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