Completely Regular Spaces

Some articles on space, completely regular spaces, completely, completely regular:

Tychonoff Space - Properties - Real-valued Continuous Functions
... For any topological space X, let C(X) denote the family of real-valued continuous functions on X and let C*(X) be the subset of bounded real-valued continuous functions ... Completely regular spaces can be characterized by the fact that their topology is completely determined by C(X) or C*(X) ... In particular A space X is completely regular if and only if it has the initial topology induced by C(X) or C*(X) ...

Famous quotes containing the words spaces, completely and/or regular:

    We should read history as little critically as we consider the landscape, and be more interested by the atmospheric tints and various lights and shades which the intervening spaces create than by its groundwork and composition.
    Henry David Thoreau (1817–1862)

    In a completely sane world, madness is the only freedom!
    —J.G. (James Graham)

    “I couldn’t afford to learn it,” said the Mock Turtle with a sigh. “I only took the regular course.”
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    Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)