| dbp:mathStatement
|
- Let be a linear map between two locally convex Hausdorff spaces and If is the inductive limit of an arbitrary family of Banach spaces, if is a K-analytic space, and if the graph of is closed in then is continuous. (en)
- A linear operator from a barrelled space to a Fréchet space is continuous if and only if its graph is closed. (en)
- A closed and bounded linear map from a locally convex infrabarreled space into a complete pseudometrizable locally convex space is continuous. (en)
- Let be linear map between two locally convex Hausdorff spaces and If is the inductive limit of an arbitrary family of Banach spaces, if is a Souslin space, and if the graph of is a Borel set in then is continuous. (en)
- Also, a closed linear map from a locally convex ultrabarrelled space into a complete pseudometrizable TVS is continuous. (en)
- Suppose that and are two topological vector spaces with the following property:
:If is any closed subspace of and is any continuous map of onto then is an open mapping.
Under this condition, if is a linear map whose graph is closed then is continuous. (en)
- Suppose that is a linear map whose graph is closed.
If is an inductive limit of Baire TVSs and is a webbed space then is continuous. (en)
- If is a linear map between two F-spaces, then the following are equivalent:
# is continuous.
# has a closed graph.
# If in and if converges in to some then
# If in and if converges in to some then (en)
- A closed surjective linear map from a complete pseudometrizable TVS onto a locally convex ultrabarrelled space is continuous. (en)
- A linear map between two F-spaces is continuous if and only if its graph is closed. (en)
|
