In functional analysis and related areas of mathematics, a sequence space is an important class of function space.
The set of all functions from the natural numbers to complex numbers, which can naturally be identified with the set of all possible sequences of elements of 
, can be turned into a vector space. Any linear subspace of this space is then called sequence space.
A sequence space equipped with the topology of pointwise convergence is called FK-space.
Definition
We identify the set of all functions
with the set of all sequences
with 
This set can be turned into a vector space by defining vector addition as
and the scalar multiplication as
A sequence space X is a linear subspace of ω.
Examples
- c the space of all convergent, real valued sequences
See also