Topological vector space

Dense basis

A dense basis¹ B of a Topological vector space 𝑉 is a linearly independent set such that fun

𝑉=Cl⁡span⁡B

i.e. a vector basis for a dense subspace of 𝑉. See also Orthonormal dense basis.

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d\Spanp | en | SemBr

Footnotes

1. This is nonstandard terminology. Normally, this is just called a basis, while the normal definition of a basis is relegated to Hammel basis. ↩