Totally Bounded Space
In topology and related branches of mathematics, a totally bounded space is a space that can be covered by finitely many subsets of any fixed "size" (where the meaning of "size" depends on the given context). The smaller the size fixed, the more subsets may be needed, but any specific size should require only finitely many subsets. A related notion is a totally bounded set, in which only a subset of the space needs to be covered. Every subset of a totally bounded space is a totally bounded set; but even if a space is not totally bounded, some of its subsets still will be.
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Famous quotes containing the words totally, bounded and/or space:
“However great a man’s fear of life, suicide remains the courageous act, the clear-headed act of a mathematician. The suicide has judged by the laws of chance—so many odds against one that to live will be more miserable than to die. His sense of mathematics is greater than his sense of survival. But think how a sense of survival must clamour to be heard at the last moment, what excuses it must present of a totally unscientific nature.”
—Graham Greene (1904–1991)
“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)
“If we remembered everything, we should on most occasions be as ill off as if we remembered nothing. It would take us as long to recall a space of time as it took the original time to elapse, and we should never get ahead with our thinking. All recollected times undergo, accordingly, what M. Ribot calls foreshortening; and this foreshortening is due to the omission of an enormous number of facts which filled them.”
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