In mathematics, compactly generated can refer to:

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Compactly generated space

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

Compactly generated group

mathematics, a compactly generated (topological) group is a topological group G which is algebraically generated by one of its compact subsets. This should

Triangulated category

explain the name: if a localizing subcategory S of a compactly generated triangulated category D is generated by a set of objects, then there is a Bousfield

Compact object (mathematics)

D({\text{Sh}}(X;{\text{Ab}}))} for a non-compact topological space X {\displaystyle X} , it is generally not a compactly generated category. Some evidence for this

Category of compactly generated weak Hausdorff spaces

In mathematics, the category of compactly generated weak Hausdorff spaces, CGWH, is a category used in algebraic topology as an alternative to the category

Compact-open topology

coincides with the compact-open topology and may be used to uniquely define it. The modification of the definition for compactly generated spaces may be viewed

CW complex

that X and Y are compactly generated Hausdorff spaces, so Hom(X,Y) is often taken with the compactly generated variant of the compact-open topology; the

Weak Hausdorff space

often used in tandem with compactly generated spaces in algebraic topology. For that, see the category of compactly generated weak Hausdorff spaces. Their