Total subset

In mathematics, more specifically in functional analysis, a subset $T$ of a topological vector space $X$ is said to be a total subset of $X$ if the linear span of $T$ is a dense subset of $X.$ [1] This condition arises frequently in many theorems of functional analysis.

Examples

Unbounded self-adjoint operators on Hilbert spaces are defined on total subsets.

See also

Dense subset – Subset whose closure is the whole space
Positive linear operator
Topological vector spaces – Vector space with a notion of nearness

References

Schaefer & Wolff 1999, p. 80.

Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.

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