# densely defined

Given a topological space $X$, we say that a map $f\colon Y\to X$ 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 $A\colon\mathscr{D}(A)\subset X\to X$ is said to be densely defined if $\mathscr{D}(A)$ is a dense vector subspace of $X$.

Title densely defined DenselyDefined 2013-03-22 13:48:12 2013-03-22 13:48:12 Koro (127) Koro (127) 7 Koro (127) Definition msc 47A05 msc 54C10