Topological Space - Topological Spaces With Order Structure

Topological Spaces With Order Structure

  • Spectral. A space is spectral if and only if it is the prime spectrum of a ring (Hochster theorem).
  • Specialization preorder. In a space the specialization (or canonical) preorder is defined by xy if and only if cl{x} ⊆ cl{y}.

Read more about this topic:  Topological Space

Famous quotes containing the words spaces, order and/or structure:

    Every true man is a cause, a country, and an age; requires infinite spaces and numbers and time fully to accomplish his design;—and posterity seem to follow his steps as a train of clients.
    Ralph Waldo Emerson (1803–1882)

    Man is clearly made to think. It is his whole dignity and his whole merit; and his whole duty is to think as he ought. And the order of thought is to begin with ourselves, and with our Author and our end.
    Blaise Pascal (1623–1662)

    Man is more disposed to domination than freedom; and a structure of dominion not only gladdens the eye of the master who rears and protects it, but even its servants are uplifted by the thought that they are members of a whole, which rises high above the life and strength of single generations.
    Karl Wilhelm Von Humboldt (1767–1835)