Question

What is Bonach space?

Answer 1

A Banach space is a complete vector space with a norm . ... An infinite-dimensional space can have many different norms. A basic example is -dimensional Euclidean space with the Euclidean norm. Usually, the notion of Banach space is only used in the infinite dimensional setting, typically as a vector space of functions.

Answer 2

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.

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