Definition of Pseudometrizable. Meaning of Pseudometrizable. Synonyms of Pseudometrizable

- form a basis for the topology. A topological space is said to be a pseudometrizable space if the space can be given a pseudometric such that the pseudometric...
- functional analysis and related areas of mathematics, a metrizable (resp. pseudometrizable) topological vector space (TVS) is a TVS whose topology is induced...
- {\displaystyle y=0.} Every metrizable topological space is pseudometrizable. A pseudometrizable space is metrizable if and only if it is Hausdorff. Closed...
- there is an equivalent metric that is translation-invariant. A TVS is pseudometrizable if and only if it has a countable neighborhood basis at the origin...
- X^{\prime }.} If X {\displaystyle X} is a sequential space (such as a pseudometrizable space) then this list may be extended to include: F {\displaystyle...
- {\displaystyle A:X\to Y} be a continuous linear operator from a complete pseudometrizable TVS X {\displaystyle X} onto a Hausdorff TVS Y . {\displaystyle Y.}...
- is Tychonoff. Every topological group is completely regular. Every pseudometrizable space is completely regular, but not Tychonoff if the space is not...
- this context. If the domain is a bornological space (for example, a pseudometrizable TVS, a Fréchet space, a normed space) then a linear operators into...
- \left(X,p_{D}\right)} into a seminormed space that carries its canonical pseudometrizable topology. The set of scalar multiples r D {\displaystyle rD} as r {\displaystyle...
- induced by some seminorm. In particular, every locally bounded TVS is pseudometrizable. Let f : X → Y {\displaystyle f:X\to Y} a function between topological...