Editing Spectral space (section)

==Spectral maps==
A '''spectral map''' ''f: X → Y'' between spectral spaces ''X'' and ''Y'' is a [[continuous map]] such that the [[preimage]] of every open and compact subset of ''Y'' under ''f'' is  again compact.

The [[category (mathematics)|category]] of spectral spaces, which has spectral maps as morphisms, is [[Equivalence of categories|dually equivalent]] to the category of bounded distributive lattices (together with [[homomorphism]]s of such lattices).{{sfn|Johnstone|1982}} In this anti-equivalence, a spectral space ''X'' corresponds to the lattice ''K''<sup><math>\circ</math></sup>(''X'').