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.
Comments (0)