 Riesz's lemma

If $Y$ is a proper closed subspace of a normed space $X$ and $0<\alpha <1$, there is a unit vector $x\in X$ whose distance from $Y$ exceeds $\alpha$.

Riesz's lemma is a result in functional analysis that deals with the structure of certain topological vector spaces, particularly in the context of Banach spaces. It can be used to construct a specific type of vector in relation to a closed subspace of a Banach space.