Definition 5.13.1. A topological space $X$ is called locally quasi-compact1 if every point has a fundamental system of quasi-compact neighbourhoods.

[1] This may not be standard notation. Alternative notions used in the literature are: (1) Every point has some quasi-compact neighbourhood, and (2) Every point has a closed quasi-compact neighbourhood. A scheme has the property that every point has a fundamental system of open quasi-compact neighbourhoods.

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