Total subset

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


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

See also[edit]


  • 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.