densely defined

Given a topological space $X$, we say that a map $f:Y\to X$ is densely defined if its domain $Y$ is a dense subset of $X$.

This terminology is commonly used in the of linear operators with the following meaning: In a normed space $X$, a linear operator $A:𝒟(A)\subset X\to X$ is said to be densely defined if $𝒟(A)$ is a dense vector subspace of $X$.