How would I express the statement "Let H be a subspace of V" in mathematical notation?

Question

How would I express the statement "Let H be a subspace of V" in mathematical notation? Does something like this work? $$ ( \ \ H(\mathbb{R})\subset V(\mathbb{R}) \ ) $$

Answer 1

The clearest way is to simply use "Let $H$ be a subspace of $V$". Then there is no need to use any specially defined notation.

Answer 2

In such a simple way, it suffices to write let $H$ be a subspace of $V$. In the context of "chains" of subspaces, you can introduce a terminology like

For vector spaces $U, V$ we write $$U\le V \quad :\Leftrightarrow U \text{ is a (closed) subspace of } V$$

This allows for more convenient notations like $$V_1 \le V_2 \le \ldots \le V_n\le H$$ For Galerkin-type algorithms (working on a chain of finite-dimensional closed subspaces)