| 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) |
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https://www.ams.org/%7Cjournal=Proceedings |
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dbr:Q.E.D. dbr:Barrelled_space dbr:Uniform_boundedness_principle dbr:Complete_topological_vector_space dbr:Convex_analysis dbr:Convex_series dbc:Theorems_in_functional_analysis dbr:Closed_graph_theorem dbr:Closed_graph_theorem_(functional_analysis) dbr:Fréchet_space dbc:Theorems_involving_convexity dbr:Convex_function dbr:Locally_convex_topological_vector_space dbr:Functional_analysis dbr:Topological_vector_space dbr:Linear_span dbr:Algebraic_interior dbr:Normed_space dbr:First_countable dbr:Jim_Simons_(mathematician) dbr:Interior_(topology) dbr:Metrizable_topological_vector_space dbr:Open_map dbr:Open_mapping_theorem_(functional_analysis) dbr:Series_(mathematics) dbr:Multivalued_function dbr:Affine_span dbr:Barreled_space dbr:First_countable_space dbr:Closed_(mathematics) dbr:Multifunction |
| 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 |
dbr:Uniform_boundedness_principle dbr:Closed_graph_theorem dbr:Open_mapping_theorem_(functional_analysis) Theorem (en) Corollary (en) Robinson–Ursescu theorem (en) Simons' theorem (en) |
| dbp:note |
Ursescu (en) |
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dbc:Theorems_in_functional_analysis dbc:Theorems_involving_convexity |
| 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 |
Ursescu theorem (en) |
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wikidata:Ursescu theorem https://global.dbpedia.org/id/BuN7M |
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wikipedia-en:Ursescu_theorem?oldid=1119690314&ns=0 |
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wikipedia-en:Ursescu_theorem |
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dbr:Robinson-Ursescu_theorem dbr:Robinson–Ursescu_theorem dbr:Simons'_theorem |
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dbr:Robinson-Ursescu_theorem dbr:Robinson–Ursescu_theorem dbr:Algebraic_interior dbr:Jim_Simons_(mathematician) dbr:Simons'_theorem |
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