(mathematics) | Banach space - A complete normed vector space. Metric is
induced by the norm: d(x,y) = ||x-y||. Completeness means
that every Cauchy sequence converges to an element of the
space. All finite-dimensional real and complex normed
vector spaces are complete and thus are Banach spaces.Using absolute value for the norm, the real numbers are a Banach space whereas the rationals are not. This is because there are sequences of rationals that converges to irrationals. Several theorems hold only in Banach spaces, e.g. the Banach inverse mapping theorem. All finite-dimensional real and complex vector spaces are Banach spaces. Hilbert spaces, spaces of integrable functions, and spaces of absolutely convergent series are examples of infinite-dimensional Banach spaces. Applications include wavelets, signal processing, and radar. [Robert E. Megginson, "An Introduction to Banach Space Theory", Graduate Texts in Mathematics, 183, Springer Verlag, September 1998]. |

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Banach algebra

Banach inverse mapping theorem

**-- Banach space --**

Banach-Tarski paradox

Banal

Banality

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banana peel

banana problem

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banana republic

banana skin

bamboo fern

bamboo palm

Bamboo partridge

Bamboo rat

bamboo shoot

Bamboozle

Bamboozler

Bambusa

Bambusa vulgaris

Bambuseae

bamf

Ban

Ban of the empire

Banach algebra

Banach inverse mapping theorem

Banach-Tarski paradox

Banal

Banality

Banana

Banana bird

banana boat

banana bread

banana family

banana label

banana oil

banana passion fruit

banana peel

banana problem

banana quit

banana republic

banana skin