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

References

Schaefer 1999, p. 80.

Schaefer, Helmut H. (1999). Topological Vector Spaces. GTM. 3. New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.CS1 maint: ref=harv (link)

Functional analysis (topics – glossary)

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Properties	barrelled complete dual (algebraic/topological) locally convex reflexive separable

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