Topological Group - Relationship To Other Areas of Mathematics

Relationship To Other Areas of Mathematics

Of particular importance in harmonic analysis are the locally compact groups, because they admit a natural notion of measure and integral, given by the Haar measure. The theory of group representations is almost identical for finite groups and for compact topological groups. In general, σ-compact Baire topological groups are locally compact.

Read more about this topic:  Topological Group

Famous quotes containing the words relationship, areas and/or mathematics:

    Living in cities is an art, and we need the vocabulary of art, of style, to describe the peculiar relationship between man and material that exists in the continual creative play of urban living. The city as we imagine it, then, soft city of illusion, myth, aspiration, and nightmare, is as real, maybe more real, than the hard city one can locate on maps in statistics, in monographs on urban sociology and demography and architecture.
    Jonathan Raban (b. 1942)

    The discovery of the North Pole is one of those realities which could not be avoided. It is the wages which human perseverance pays itself when it thinks that something is taking too long. The world needed a discoverer of the North Pole, and in all areas of social activity, merit was less important here than opportunity.
    Karl Kraus (1874–1936)

    The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.
    Willard Van Orman Quine (b. 1908)