Compact Group

Compact Group

In mathematics, a compact (topological, often understood) group is a topological group whose topology is compact. Compact groups are a natural generalisation of finite groups with the discrete topology and have properties that carry over in significant fashion. Compact groups have a well-understood theory, in relation to group actions and representation theory.

In the following we will assume all groups are Hausdorff spaces.

Read more about Compact Group:  Compact Lie Groups, Further Examples, Haar Measure, Representation Theory, Duality, From Compact To Non-compact Groups

Famous quotes containing the words compact and/or group:

    Take pains ... to write a neat round, plain hand, and you will find it a great convenience through life to write a small and compact hand as well as a fair and legible one.
    Thomas Jefferson (1743–1826)

    The virtue of dress rehearsals is that they are a free show for a select group of artists and friends of the author, and where for one unique evening the audience is almost expurgated of idiots.
    Alfred Jarry (1873–1907)