### Some articles on *totally bounded, totally*:

Glossary Of Topology - T

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**Totally bounded**A metric space M is**totally bounded**if, for every r > 0, there exist a finite cover of M by open balls of radius r ... compact if and only if it is complete and**totally bounded**...**Totally**disconnected A space is**totally**disconnected if it has no connected subset with more than one point ...Uniform Property - Uniform Properties

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**Totally bounded**(or Precompact) ... A uniform space X is**totally bounded**if for each entourage E ⊂ X × X there is a finite cover {Ui} of X such that Ui × Ui is contained in E for all i ... Equivalently, X is**totally bounded**if for each entourage E there exists a finite subset {xi} of X such that X is the union of all E ...**Totally Bounded**Space - Use of The Axiom of Choice

... does not require choice) that every precompact space is

**totally bounded**in other words, if the completion of a space is compact, then that space is

**totally bounded**... (that is, the proof requires choice) that every

**totally bounded**space is precompact in other words, the completion of a

**totally bounded**space might not be compact in the absence of choice ...

### Famous quotes containing the words bounded and/or totally:

“I could be *bounded* in a nutshell and count myself a king of

infinite space, were it not that I have bad dreams.”

—William Shakespeare (1564–1616)

“Postmodernism is, almost by definition, a transitional cusp of social, cultural, economic and ideological history when modernism’s high-minded principles and preoccupations have ceased to function, but before they have been replaced with a *totally* new system of values. It represents a moment of suspension before the batteries are recharged for the new millennium, an acknowledgment that preceding the future is a strange and hybrid interregnum that might be called the last gasp of the past.”

—Gilbert Adair, British author, critic. Sunday Times: Books (London, April 21, 1991)

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