Compactly generated space
In topology, a topological space X {\displaystyle X} is called a compactly generated space or k-space if its topology is determined by compact spaces in a manner made precise below. There is in fact no commonly agreed upon definition for such spaces, as different authors use variations of the definition that are not exactly equivalent to each other.
Source: Wikipedia — Compactly generated space (CC BY-SA 4.0)