I am require to show that every finite-dimensional subspace of the inner product space $(V,\langle\cdot,\cdot\rangle)$ is a closed subset of $V$, with respect to the metric $d$ where $d(u,v) = ||u-v||$.
My main problem is that the definition of a closed subset is not give. So to cut things short How do we define a closed subset of $V$, for some context I found this in my Linear Algebra text book in the Chapter that introduces Inner Product Spaces.