Definition:Vector Space of Sequences with Finite Support

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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


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