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densely defined (Definition)

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 theory 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$.



"densely defined" is owned by Koro.
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Cross-references: vector subspace, dense, normed space, linear operators, dense subset, domain, map, topological space
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This is version 4 of densely defined, born on 2003-07-28, modified 2006-06-15.
Object id is 4523, canonical name is DenselyDefined.
Accessed 2970 times total.

Classification:
AMS MSC: 54C10 (General topology :: Maps and general types of spaces defined by maps :: Special maps on topological spaces )
 47A05 (Operator theory :: General theory of linear operators :: General )
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