- TVS is
normable if and only if it is
seminormable and
Hausdorff or equivalently, if and only if it is
seminormable and T1 (because a TVS is
Hausdorff if...
-
bounded subsets of Y {\displaystyle Y} ). If Y {\displaystyle Y} is
seminormable space (such as a
normed space) then this list may be
extended to include:...
- {\displaystyle 0<p\leq 1,} a
topological vector space is p {\displaystyle p} -
seminormable (meaning that its
topology is
induced by some p {\displaystyle p} -seminorm)...
-
single seminorm, then the
space is
seminormable. Any
locally convex space with a
finite family of
seminorms is
seminormable. Moreover, if the
space is Hausdorff...
- norm, normable, normal, normality, normative, quasinorm, seminorm,
seminormable, seminormal,
subnormal not-
south Gr**** νότος (nótos) Notogaea, Notomys...
-
metrizable TVS.
Kolmogorov used this
definition to
prove that a TVS is
seminormable if and only if it has a
bounded convex neighborhood of the origin. For...
-
topology is a
compact (and thus
locally compact)
complete pseudometrizable seminormable locally convex topological vector space. It is
Hausdorff if and only...
- norm, normable, normal, normality, normative, quasinorm, seminorm,
seminormable, seminormal,
subnormal not-
south Gr**** νότος (nótos) Notogaea, Notomys...
- its completion:
Hausdorff Locally convex Pseudometrizable Metrizable Seminormable Normable Moreover, if ( X , p ) {\displaystyle (X,p)} is a
normed space...
- bornological, (2) infrabarreled, (3) barreled. A
topological vector space is
seminormable if and only if it has a
convex bounded neighborhood of the origin. Moreover...
