# Normed vector spaces

///////

• …

///////

Related KMR-pages:

///////

Other relevant sources of information:

///////

Spaces of countably infinite dimensions
(Sequence spaces and spaces of periodic functions)

Quoting Wikipedia (on Sequence spaces):

In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication. All sequence spaces are linear subspaces of this space. Sequence spaces are typically equipped with a norm, or at least the structure of a topological vector space.

The most important sequence spaces in analysis are the $\, ℓ^p$ spaces, consisting of the p-power summable sequences, with the p-norm. These are special cases of $\, L^p \,$ spaces for the counting measure on the set of natural numbers. Other important classes of sequences like convergent sequences or null sequences form sequence spaces, respectively denoted $\, c \,$ and $\, c_0$, with the sup norm. Any sequence space can also be equipped with the topology of pointwise convergence, under which it becomes a special kind of Fréchet space called FK-space.

/////// End of quote from Wikipedia

26 types of mathematical spaces:

Spaces of uncountably infinite dimensions
(Spaces of non-periodic functions)

///////