I was wondering if linear manifold is a pure algebraic concept? Here is its definition from planetmath:
Suppose $V$ is a vector space and suppose that $L$ is a non-empty subset of $V$. If there exists a $v \in V$ such that $L+v=\{v+l, l \in L\}$ is a vector subspace of $V$ , then $L$ is a linear manifold of $V$.
If yes, why is there a "manifold" (which is a topological space) in its name?
Or is it a topological vector space with some topology unspecified but assumed
Thanks!