Last Updated：2025/12/06

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(topology) A topological group whose underlying topology is both locally compact and Hausdorff.

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locally compact group

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Source Word

locally compact group

Noun

(topology) A topological group whose underlying topology is both locally compact and Hausdorff.

Japanese Meaning

局所コンパクト群：その基底となる位相が局所コンパクトかつHausdorffとなる位相群。 / 位相群の一種であり、各点にコンパクトな近傍を持つ（局所コンパクト）と同時に、区別可能（Hausdorff）の性質を備えた群。

What is this buttons?

The representation theory of a locally compact group often reveals deep connections between analysis and geometry.

Google Translation / DeepL Translation

基礎となる位相が局所コンパクトでハウスドルフである位相群の表現論は、多くの場合、解析と幾何学の間の深い関係を明らかにする。

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(topology) A topological group whose underlying topology is both locally compact and Hausdorff.

Indeed, if there is one property of locally compact groups more responsible than any other for the rich positive content of their representation theory, it is their possession of left-invariant and right-invariant (Haar) measures. The connection between the representation theory of a locally compact group and that of general Banach algebras proceeds directly from Lebesgue integration with respect to Haar measure on the group.

Google Translation / DeepL Translation

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locally compact groups

（ plural ）

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locally compact group

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