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

... 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.”

“What was that?” inquired Alice.

“Reeling and Writhing, of course, to begin with,” the Mock Turtle replied; “and then the different branches of Arithmetic—Ambition, Distraction, Uglification, and Derision.”

“I never heard of ‘Uglification,’” Alice ventured to say.”

—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)