Definition 61.2.3 (096A)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 61: Pro-étale Cohomology
Section 61.2: Some topology
Definition 61.2.3 (cite)

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Definition 61.2.3. A spectral space $X$ is w-local if the set of closed points $X_0$ is closed and every point of $X$ specializes to a unique closed point. A continuous map $f : X \to Y$ of w-local spaces is w-local if it is spectral and maps any closed point of $X$ to a closed point of $Y$ .

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