Let $X$ be a D11: Set.
Let $\mathcal{T}$ be a D86: Topology on $X$.
A D11: Set $\mathcal{S}$ is a subtopology of $\mathcal{T}$ on $X$ if and only if

(1)	$\mathcal{S} \subseteq \mathcal{T}$ (D78: Subset)
(2)	$\mathcal{S}$ is a D86: Topology on $X$