About: Ursescu theorem

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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.

Attributes	Values
rdfs:label	Ursescu theorem (en)
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)
name	Uniform boundedness principle Closed graph theorem Open mapping theorem (functional analysis) Theorem (en) Corollary (en) Robinson–Ursescu theorem (en) Simons' theorem (en)
dcterms:subject	Theorems in functional analysis Theorems involving convexity
Wikipage page ID	63556609 (xsd:integer)
Wikipage revision ID	1119690314 (xsd:integer)
Link from a Wikipage to another Wikipage	Q.E.D. Barrelled space Uniform boundedness principle Complete topological vector space Convex analysis Convex series Theorems in functional analysis Closed graph theorem Closed graph theorem (functional analysis) Fréchet space Theorems involving convexity Convex function Locally convex topological vector space Functional analysis Topological vector space Linear span Algebraic interior Normed space First countable Jim Simons (mathematician) Interior (topology) Metrizable topological vector space Open map Open mapping theorem (functional analysis) Series (mathematics) Multivalued function Affine span Barreled space First countable space Closed (mathematics) Multifunction
Link from a Wikipage to an external page	https://www.ams.org/%7Cjournal=Proceedings
sameAs	Ursescu theorem Ursescu theorem
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_journal dbt:Reflist dbt:Sfn dbt:Short_description dbt:Math_proof dbt:Convex_analysis_and_variational_analysis dbt:Functional_analysis dbt:Math_theorem dbt:Topological_vector_spaces dbt:Zălinescu_Convex_Analysis_in_General_Vector_Spaces_2002
note	Ursescu (en)
has 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)
math statement	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)
prov:wasDerivedFrom	wikipedia-en:Ursescu_theorem?oldid=1119690314&ns=0
page length (characters) of wiki page	13191 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Ursescu_theorem
is Link from a Wikipage to another Wikipage of	Robinson-Ursescu theorem Robinson–Ursescu theorem Algebraic interior Jim Simons (mathematician) Simons' theorem
is Wikipage redirect of	Robinson-Ursescu theorem Robinson–Ursescu theorem Simons' theorem
is foaf:primaryTopic of	wikipedia-en:Ursescu_theorem

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