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If a vector space V has a subset M such that M [union] {0} contains an infinite-dimensional vector space, then M is called lineable. If M [union] {0} contains a closed infinite-dimensional vector space, then M is called spaceable.
We have that {T [member of] L(X) such that T is injective} is lineable.
As it nowadays is common terminology, a subset M of a topological vector space X is called lineable (respectively, spaceable) in X if there exists an infinite dimensional linear space (respectively, infinite dimensional closed linear space) Y [subset] M [union] {0}.