In mathematics, compactly generated can refer to:

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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

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

Finitely generated group

finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation)

List of group theory topics

group Commensurability (group theory) Compact group Compactly generated group Complete group Complex reflection group Congruence subgroup Continuous symmetry

Compact object (mathematics)

condition of being compact is quite strong, so that most objects are not compact. A category C {\displaystyle C} is compactly generated if any object can

Compact quantum group

In mathematics, compact quantum groups are generalisations of compact groups, where the commutative C ∗ {\displaystyle \mathrm {C} ^{*}} -algebra of continuous

Boundedly generated group

boundedly generated, then so is G itself. Any quotient group of a boundedly generated group is also boundedly generated. A finitely generated torsion group must

Locally compact space

locally compact Hausdorff spaces are compactly generated. Conversely, every compactly generated Hausdorff space is a quotient of some locally compact Hausdorff