| dbo:abstract
|
- In mathematics, particularly in functional analysis and convex analysis, the Ursescu theorem is a theorem that generalizes the closed graph theorem, the open mapping theorem, and the uniform boundedness principle. (en)
|
| dbo:wikiPageExternalLink
| |
| dbo:wikiPageID
| |
| dbo:wikiPageLength
|
- 13191 (xsd:nonNegativeInteger)
|
| dbo:wikiPageRevisionID
| |
| dbo:wikiPageWikiLink
| |
| dbp:mathStatement
|
- Let and be Fréchet spaces and be a continuous surjective linear map. Then T is an open map. (en)
- Let and be Fréchet spaces and be a bijective linear map. Then is continuous if and only if is continuous. Furthermore, if is continuous then is an isomorphism of Fréchet spaces. (en)
- Let be a barreled first countable space and let be a subset of Then:
# If is lower ideally convex then
# If is ideally convex then (en)
- Let and be normed spaces and be a multimap with non-empty domain.
Suppose that is a barreled space, the graph of verifies condition condition (Hwx), and that
Let denote the closed unit ball in .
Then the following are equivalent:
# belongs to the algebraic interior of
#
# There exists such that for all
# There exist and such that for all and all
# There exists such that for all and all (en)
- Let and be Fréchet spaces and be a linear map. Then is continuous if and only if the graph of is closed in (en)
- Let and be first countable with locally convex. Suppose that is a multimap with non-empty domain that satisfies condition (Hwx) or else assume that is a Fréchet space and that is lower ideally convex.
Assume that is barreled for some/every
Assume that and let
Then for every neighborhood of in belongs to the relative interior of in .
In particular, if then (en)
- Let be a complete semi-metrizable locally convex topological vector space and be a closed convex multifunction with non-empty domain.
Assume that is a barrelled space for some/every
Assume that and let .
Then for every neighborhood of in belongs to the relative interior of in .
In particular, if then (en)
|
| dbp:name
| |
| dbp:note
| |
| dbp:wikiPageUsesTemplate
| |
| dcterms:subject
| |
| rdfs:comment
|
- In mathematics, particularly in functional analysis and convex analysis, the Ursescu theorem is a theorem that generalizes the closed graph theorem, the open mapping theorem, and the uniform boundedness principle. (en)
|
| rdfs:label
| |
| owl:sameAs
| |
| prov:wasDerivedFrom
| |
| foaf:isPrimaryTopicOf
| |
| is dbo:wikiPageRedirects
of | |
| is dbo:wikiPageWikiLink
of | |
| is foaf:primaryTopic
of | |
