Definition 5.23.1 (08YG)—The Stacks project

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Part 1: Preliminaries
Chapter 5: Topology
Section 5.23: Spectral spaces
Definition 5.23.1 (cite)

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Definition 5.23.1. A topological space $X$ is called spectral if it is sober, quasi-compact, the intersection of two quasi-compact opens is quasi-compact, and the collection of quasi-compact opens forms a basis for the topology. A continuous map $f : X \to Y$ of spectral spaces is called spectral if the inverse image of a quasi-compact open is quasi-compact.

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Comment #9858 by Yaël Dillies on November 12, 2024 at 13:40

The definition of a spectral map seems to be exactly the same as that of quasi-compact map from 005A.

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