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
Canonical name	DenselyDefined
Date of creation	2013-03-22 13:48:12
Last modified on	2013-03-22 13:48:12
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	7
Author	Koro (127)
Entry type	Definition
Classification	msc 47A05
Classification	msc 54C10