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 $$X.$$ This condition arises frequently in many theorems of functional analysis.

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