Continuously embedded
From Wikipedia, the free encyclopedia
In mathematics, one normed vector space is said to be continuously embedded in another normed vector space if the inclusion function between them is continuous. In some sense, the two norms are "almost equivalent", even though they are not both defined on the same space. Several of the Sobolev embedding theorems are continuous embedding theorems.
[edit] Definition
Let X and Y be two normed vector spaces, with norms 
and 
respectively, such that 
. If the inclusion map
is continuous, i.e. if there exists a constant 
such that
for every 
, then X is continuously embedded in Y.
[edit] See also
[edit] Reference
- Rennardy, M., & Rogers, R.C. (1992). An Introduction to Partial Differential Equations. Springer-Verlag, Berlin. ISBN 3-540-97952-2.
