Definition:Vector Space of Sequences with Finite Support

Definition
Let $\struct {K, +, \circ}$ be a division ring.

Let $K^\N$ be the set of sequences $\sequence{ a_n }_{n \in \N}$ in $K$.

Regard $K^\N$ as a vector space of all mappings from $\N$ to $K$.

The vector space of sequences with finite support is the vector subspace of $K^\N$ of sequences with finite support:


 * $\ds \set{ f \in K^\N: \text{$f$ has finite support} }$

There is no standard symbol for the vector space of sequences with finite support.

Also see

 * Vector Space of Sequences with Finite Support is Vector Space