Weakly Compact

Weakly compact can refer to:

  • Weakly compact cardinal, an infinite cardinal number on which every binary relation has an equally large homogeneous subset
  • Weakly compact set, a compact set in a space with the weak topology
  • Weakly compact set, a set that has some but not all of the properties of compact sets, for example:
    • Sequentially compact space, a set in which every infinite sequence has a convergent subsequence
    • Limit point compact, a set in which every infinite subset of X has a limit point

Famous quotes containing the words weakly and/or compact:

    “If a weakly mortal is to do anything in the world besides eat the bread thereof, there must be a determined subordination of the whole nature to the one aim—no trifling with time, which is passing, with strength which is only too limited.”
    —Beatrice Potter Webb (1858–1943)

    “The powers of the federal government ... result from the compact to which the states are parties, [and are] limited by the plain sense and intention of the instrument constituting that compact.”
    —James Madison (1751–1836)