Tychonoff Spaces

Some articles on space, spaces:

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 word spaces:

    Though there were numerous vessels at this great distance in the horizon on every side, yet the vast spaces between them, like the spaces between the stars,—far as they were distant from us, so were they from one another,—nay, some were twice as far from each other as from us,—impressed us with a sense of the immensity of the ocean, the “unfruitful ocean,” as it has been called, and we could see what proportion man and his works bear to the globe.
    Henry David Thoreau (1817–1862)