The spectral theory of distributive continuous lattices

Karl H. Hofmann, Jimmie D. Lawson
1978 Transactions of the American Mathematical Society  
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
more » ... h topology is extended from algebraic lattices to continuous lattices, and necessary and sufficient conditions for its compactness are given.
doi:10.1090/s0002-9947-1978-0515540-7 fatcat:jkofdllhkncqjk2zw3yoysmcfm