Let $P = (Y, {\leq})$ be a D1103: Partially ordered set.
Let $f : X \to Y$ be a D18: Map.
The strict sublevel set of $f$ with respect to $y \in Y$ and $P$ is the D11: Set \begin{equation} \{ f < y \} : = \{ x \in X : f(x) < y \} \end{equation}