[[Topological vector space]]
# Dense basis

A **dense basis**[^term] $\mathcal{B}$ of a [[Topological vector space]] $V$ is a [[Linear (in)dependence|linearly independent]] set such that #m/def/anal/fun
$$
\begin{align*}
V = \Cl \Span \mathcal{ B}
\end{align*}
$$
i.e. a [[vector basis]] for a [[Dense set|dense]] subspace of $V$.
See also [[Orthonormal dense basis]].

  [^term]: This is nonstandard terminology. Normally, this is just called a basis, while the normal definition of a basis is relegated to [[Vector basis|Hammel basis]].

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#state/d\Spanp | #lang/en | #SemBr