nLab
diagram of LCTVS properties

LCTVS cluster_key_col1 cluster_key_col2 cluster_key_col3 FD FD Hi Hi FD->Hi NuFr FD->NuFr IP IP Hi->IP ReBa Hi->ReBa Nu Nu Sc Sc Nu->Sc Ba Ba Fr Fr Ba->Fr No No Ba->No LB LB Ba->LB IP->No Mo Mo Re Re Mo->Re UB UB Bo Bo UB->Bo QCQB UB->QCQB LF LF Fr->LF Me Me Fr->Me Pt Pt Fr->Pt DF DF No->DF No->Me QB QB Bo->QB LF->UB LB->DF LB->LF Me->Bo NuFr->Nu NuFr->Mo ReFr NuFr->ReFr LC LC QC QC Sq Sq QC->Sq BC BC Pt->BC Cp Cp BC->Cp Sq->LC Cp->QC Bl Bl Re->Bl MkSR Re->MkSR SR SR SR->QC Mk Mk QB->Mk Bl->QB MkSR->SR MkSR->Mk QCQB->QC QCQB->Bl ReBa->Ba ReBa->ReFr ReFr->Fr ReFr->Re yFD yHi xFD FD: Finite-Dimensional yDF Key to symbols yNo xDF DF: DF yPt yBC xPt Pt: Ptak Space yNu xHi Hi: Hilbert (technically, admits a Hilbertian structure) yBa xNu Nu: Nuclear yIP xBa Ba: Banach (technically, complete and normable) yMo xIP IP: Topology from an inner-product ySc xMo Mo: Montel yUB xSc Sc: Schwartz yFr xUB UB: Ultrabornological yZ1 xFr Fr: Fréchet yBo xNo No: Normable space yLF xBo Bo: Bornological yLB xLF LF: strict inductive sequence of Fréchet spaces yMe xLB LB: strict inductive sequence of Banach spaces yLC xMe Me: Metrisable yQC xLC LC: Locally Complete yZ2 xQC QC: Quasi-Complete ySq xBC BC: Br Space yCp xSq Sq: Sequentially Complete yRe xCp Cp: Complete ySR xRe Re: Reflexive yQB xSR SR: Semi-Reflexive yMk xQB QB: Quasi-Barrelled yBl xMk Mk: Mackey yZ3 xBl Bl: Barrelled

category: svg

Revised on October 28, 2010 08:31:07 by Toby Bartels (75.88.77.52)