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FK-space : ウィキペディア英語版
FK-space

In functional analysis and related areas of mathematics a FK-space or Fréchet coordinate space is a sequence space equipped with a topological structure such that it becomes a Fréchet space. FK-spaces with a normable topology are called BK-spaces.
There exists only one topology to turn a sequence space into a Fréchet space, namely the topology of pointwise convergence. Thus the name ''coordinate space'' because a sequence in an FK-space converges if and only if it converges for each coordinate.
FK-spaces are examples of topological vector spaces. They are important in summability theory.
==Definition==
A FK-space is a sequence space X, that is a linear subspace of vector space of all complex valued sequences, equipped with the topology of pointwise convergence.
We write the elements of X as
:(x_n)_
Then sequence (a_n)_ in X converges to some point (x_n)_ (a_n)_ = (x_n)_ : \lim_ a_n^ = x_n

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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