The spectral theory of distributive continuous lattices

Hofmann, Karl H.; Lawson, Jimmie D.

doi:10.1090/S0002-9947-1978-0515540-7

The spectral theory of distributive continuous lattices
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by Karl H. Hofmann and Jimmie D. Lawson PDF

Trans. Amer. Math. Soc. 246 (1978), 285-310 Request permission

Abstract:

In this paper various properties of the spectrum (i.e. the set of prime elements endowed with the hull-kernel topology) of a distributive continuous lattice are developed. It is shown that the spectrum is always a locally quasicompact sober space and conversely that the lattice of open sets of a locally quasicompact sober space is a continuous lattice. Algebraic lattices are a special subclass of continuous lattices and the special properties of their spectra are treated. The concept of the patch topology is extended from algebraic lattices to continuous lattices, and necessary and sufficient conditions for its compactness are given.

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Problem in “Topology and its applications"

Algebraic theories of continuous lattices