The boundedness condition for linear operators on normed spaces can be restated. Any linear operator defined on a finite-dimensional normed space is bounded. The Euclidean balls discussed earlier are an example of balls in a normed vector space. The cartesian product of two normed spaces is not canonically equipped with a norm. Not every linear operator between normed spaces is bounded. Reflexive normed spaces are Banach spaces. As a complete normed space, Hilbert spaces are by definition also Banach spaces. The most important maps between two normed vector spaces are the continuous linear maps. This is the standard topology on any normed vector space. Not all vector spaces are normed. Other examples of infinite-dimensional normed vector spaces can be found in the Banach space article. Of special interest are complete normed spaces called Banach spaces. As a norm-referenced test, the CDI was normed with public school students. Let "X" be a Banach space and "Y" a normed vector space. Let "X" be a Banach space and "Y" be a normed vector space.