In mathematics, with special application to complex analysis, a normal family is a pre-compact family of continuous functions. Informally, this means that the functions in the family are not exceedingly numerous or widely spread out; rather, they stick together in a relatively "compact" manner. It is of general interest to understand compact sets in function spaces, since these are usually truly infinite-dimensional in nature.
More formally, a family (that is, a set) F of continuous functions f defined on some complete metric space X with values in another complete metric space Y is called normal if every sequence of functions in F contains a subsequence which converges uniformly on compact subsets of X to a continuous function from X to Y.
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Famous quotes containing the words normal and/or family:
“Normality highly values its normal man. It educates children to lose themselves and to become absurd, and thus to be normal. Normal men have killed perhaps 100,000,000 of their fellow normal men in the last fifty years.”
—R.D. (Ronald David)
“As the family goes, so goes the nation and so goes the whole world in which we live.”
—John Paul II [Karol Wojtyla] (b. 1920)