- mathematics. A
normed vector space is a
vector space equipped with a norm. A
seminormed vector space is a
vector space equipped with a seminorm. A
useful variation...
- ) → ( Y , q ) {\displaystyle F:(X,p)\to (Y,q)}
between seminormed spaces is
itself a
seminormed space under the
seminorm ‖ F ‖ p , q . {\displaystyle \|F\|_{p...
- Y.} If X {\displaystyle X} and Y {\displaystyle Y} are both
normed or
seminormed spaces (with both
seminorms denoted by ‖ ⋅ ‖ {\displaystyle \|\cdot \|}...
-
original seminormed vector space, and this
quotient is a
normed vector space. It
inherits several convenient properties from the
seminormed space; see...
- r_{1},\dots ,r_{n}} are
positive real numbers.
Seminormed spaces and
topological groups In a
seminormed space, that is a
vector space with the topology...
- spaces. The
notion of
series can be
easily extended to the case of a
seminormed space. If x n {\displaystyle x_{n}} is a
sequence of
elements of a normed...
- norm ‖ ⋅ ‖ {\displaystyle \|\cdot \|} (or more generally, if it is a
seminormed space and ‖ ⋅ ‖ {\displaystyle \|\cdot \|} is
merely a seminorm), then...
-
completely regular, but not
Tychonoff if the
space is not Hausdorff.
Every seminormed space is
completely regular (both
because it is
pseudometrizable and because...
- space. In a
similar manner, a
vector space with a
seminorm is
called a
seminormed vector space. The term
pseudonorm has been used for
several related meanings...
-
neighborhood of the
origin absorbs it. In a
normed space (and even in a
seminormed space), a
subset is von
Neumann bounded if and only if it is norm bounded...
