nLab
second lctvs diagram dot source

/*

This is the graphviz source for an alternative version of the diagram at TVS relationships. The original intention was to see if it is possible to make this into a lattice. However, that would have made the diagram too unwieldy. Instead, the attempt is simply to expand and improve on the original diagram.

The current SVG can be seen at diagram of LCTVS properties.

To recreate the SVG, the whole source of this page (or just the code below) should be run through dot (note that this part of the page is actually a comment in the dot source so doesn’t get seen). For example, assuming that the source has been saved as lctvs.dot, run:

dot -Tsvg -o lctvs.svg lctvs.dot
*/
digraph LCTVS {
splines=true;
overlap=orthoyx;
// style for properties relating to size
subgraph size {
style=none;
node [shape=box, style=filled, fillcolor="#ffffbb"];
FD [tooltip="Finite-Dimensional", href="http://ncatlab.org/nlab/show/Finite-Dimensional topological vector space"];
Hi [tooltip="Hilbert (technically, admits a Hilbertian structure)", href="http://ncatlab.org/nlab/show/Hilbert space"];
Nu [tooltip="Nuclear", href="http://ncatlab.org/nlab/show/Nuclear space"];
Ba [tooltip="Banach (technically, complete and normable)", href="http://ncatlab.org/nlab/show/Banach space"];
IP [tooltip="Topology from an inner-product", href="http://ncatlab.org/nlab/show/inner-product space"];
Mo [tooltip="Montel", href="http://ncatlab.org/nlab/show/Montel space"];
Sc [tooltip="Schwartz", href="http://ncatlab.org/nlab/show/Schwartz space"];
UB [tooltip="Ultrabornological", href="http://ncatlab.org/nlab/show/ultrabornological topological vector space"];
Fr [tooltip="Fréchet", href="http://ncatlab.org/nlab/show/Fréchet space"];
DF [tooltip="DF", href="http://ncatlab.org/nlab/show/DF topological vector space"];
No [tooltip="Normable space", href="http://ncatlab.org/nlab/show/normed vector space"];
Bo [tooltip="Bornological", href="http://ncatlab.org/nlab/show/bornological topological vector space"];
LF [tooltip="strict inductive sequence of Fréchet spaces", href="http://ncatlab.org/nlab/show/LF space"];
LB [tooltip="strict inductive sequence of Banach spaces", href="http://ncatlab.org/nlab/show/LB space"];
Me [tooltip="Metrisable", href="http://ncatlab.org/nlab/show/metrisable topological vector space"];
// no label
node [shape=circle, width=.2];
NuFr [label="", tooltip="Nuclear Fréchet space", href="http://ncatlab.org/nlab/show/nuclear topological vector space"];
}
// style for properties relating to completeness
subgraph complete {
node [shape=box, style=filled, fillcolor="#bbffff"];
LC [tooltip="Locally Complete", href="http://ncatlab.org/nlab/show/locally complete topological vector space"];
QC [tooltip="Quasi-Complete", href="http://ncatlab.org/nlab/show/quasi-complete topological vector space"];
Pt [tooltip="Ptak Space", href="http://ncatlab.org/nlab/show/Ptak space"];
BC [tooltip="Br Space", href="http://ncatlab.org/nlab/show/Ptak space"];
Sq [tooltip="Sequentially Complete", href="http://ncatlab.org/nlab/show/sequentially complete topological vector space"];
Cp [tooltip="Complete", href="http://ncatlab.org/nlab/show/complete topological vector space"];
}
// style for properties relating to duality
subgraph dual {
node [shape=box, style=filled, fillcolor="#ffbbff"];
Re [tooltip="Reflexive", href="http://ncatlab.org/nlab/show/reflexive topological vector space"];
SR [tooltip="Semi-Reflexive", href="http://ncatlab.org/nlab/show/semi-reflexive topological vector space"];
QB [tooltip="Quasi-Barrelled", href="http://ncatlab.org/nlab/show/quasi-barrelled topological vector space"];
Mk [tooltip="Mackey", href="http://ncatlab.org/nlab/show/Mackey topological vector space"];
Bl [tooltip="Barrelled", href="http://ncatlab.org/nlab/show/barrelled topological vector space"];
// no label
node [shape=circle, width=.2];
MkSR [label="", tooltip="Mackey and Semi-Reflexive", href="http://ncatlab.org/nlab/show/Mackey topological vector space"];
}
// Style for nodes with no label
node [shape=circle, width=.2, style=filled, fillcolor="#ffffbb"];
QCQB [label="", tooltip="Quasi-Complete and Quasi-Barrelled", href="http://ncatlab.org/nlab/show/barreled topological vector space"];
ReBa [label="", tooltip="Reflexive Banach space", href="http://ncatlab.org/nlab/show/reflexive topological vector space"];
ReFr [label="", tooltip="Reflexive Fréchet space", href="http://ncatlab.org/nlab/show/reflexive topological vector space"];


FD -> Hi;
Hi -> IP;
IP -> No;
No -> Me;
Hi -> ReBa;
ReBa -> Ba;
Ba -> LB;
Ba -> Fr;
Fr -> Me;
Fr -> LF;
LB -> LF;
Ba -> No;
FD -> NuFr;
Nu -> Sc;
NuFr -> Nu;
NuFr -> ReFr;
NuFr -> Mo;
No -> DF;
LB -> DF;

UB -> Bo;
Bo -> QB;
Bl -> QB;
QB -> Mk;
Re -> Bl;
Re -> MkSR;
QCQB -> Bl;
MkSR -> Mk;
MkSR -> SR;

Pt -> BC;
BC -> Cp;
Cp -> QC;
QC -> Sq;
Sq -> LC;

QCQB -> QC;
ReBa -> ReFr;
ReFr -> Re;
ReFr -> Fr;

SR -> QC;

Fr -> Pt;

Mo -> Re;

Me -> Bo;

LF -> UB;
UB -> QCQB;

/*
All the rest generates the key
*/

subgraph keys {
rank=same;
yFD  [label="",width=0,style=invis];
yDF [shape=box, style=solid, label="Key to symbols"];
yPt  [label="",width=0,style=invis];
}

subgraph cluster_key_col1 {
color=white;
node [label="",width=0,style=invis];
yHi;
yNu;
yBa;
yIP;
yMo;
ySc;
yUB;
yFr;
yZ1;
}

subgraph key1 {
node [shape=box, style=filled, fillcolor="#ffffbb"];
xFD [label="FD: Finite-Dimensional", href="http://ncatlab.org/nlab/show/Finite-Dimensional topological vector space"];
xHi [label="Hi: Hilbert (technically, admits a Hilbertian structure)", href="http://ncatlab.org/nlab/show/Hilbert space"];
xNu [label="Nu: Nuclear", href="http://ncatlab.org/nlab/show/Nuclear space"];
xBa [label="Ba: Banach (technically, complete and normable)", href="http://ncatlab.org/nlab/show/Banach space"];
xIP [label="IP: Topology from an inner-product", href="http://ncatlab.org/nlab/show/inner-product space"];
xMo [label="Mo: Montel", href="http://ncatlab.org/nlab/show/Montel space"];
xSc [label="Sc: Schwartz", href="http://ncatlab.org/nlab/show/Schwartz space"];
xUB [label="UB: Ultrabornological", href="http://ncatlab.org/nlab/show/ultrabornological topological vector space"];
xFr [label="Fr: Fréchet", href="http://ncatlab.org/nlab/show/Fréchet space"];
}

subgraph cluster_key_col2 {
color=white;
node [label="",width=0,style=invis];
yNo;
yBo;
yLF;
yLB;
yMe;
yLC;
yQC;
yZ2;
}

subgraph key2 {
node [shape=box, style=filled, fillcolor="#ffffbb"];
xDF [label="DF: DF", href="http://ncatlab.org/nlab/show/DF topological vector space"];
xNo [label="No: Normable space", href="http://ncatlab.org/nlab/show/normed vector space"];
xBo [label="Bo: Bornological", href="http://ncatlab.org/nlab/show/bornological topological vector space"];
xLF [label="LF: strict inductive sequence of Fréchet spaces", href="http://ncatlab.org/nlab/show/LF space"];
xLB [label="LB: strict inductive sequence of Banach spaces", href="http://ncatlab.org/nlab/show/LB space"];
xMe [label="Me: Metrisable", href="http://ncatlab.org/nlab/show/metrisable topological vector space"];
node [shape=box, style=filled, fillcolor="#bbffff"];
xLC [label="LC: Locally Complete", href="http://ncatlab.org/nlab/show/locally complete topological vector space"];
xQC [label="QC: Quasi-Complete", href="http://ncatlab.org/nlab/show/quasi-complete topological vector space"];
}

subgraph cluster_key_col3 {
color=white;
node [label="",width=0,style=invis];
yPt;
yBC;
ySq;
yCp;
yRe;
ySR;
yQB;
yMk;
yBl;
yZ3;
}


subgraph key2 {
node [shape=box, style=filled, fillcolor="#bbffff"];
xPt [label="Pt: Ptak Space", href="http://ncatlab.org/nlab/show/Ptak space"];
xBC [label="BC: Br Space", href="http://ncatlab.org/nlab/show/Ptak space"];
xSq [label="Sq: Sequentially Complete", href="http://ncatlab.org/nlab/show/sequentially complete topological vector space"];
xCp [label="Cp: Complete", href="http://ncatlab.org/nlab/show/complete topological vector space"];
node [shape=box, style=filled, fillcolor="#ffbbff"];
xRe [label="Re: Reflexive", href="http://ncatlab.org/nlab/show/reflexive topological vector space"];
xSR [label="SR: Semi-Reflexive", href="http://ncatlab.org/nlab/show/semi-reflexive topological vector space"];
xQB [label="QB: Quasi-Barrelled", href="http://ncatlab.org/nlab/show/quasi-barrelled topological vector space"];
xMk [label="Mk: Mackey", href="http://ncatlab.org/nlab/show/Mackey topological vector space"];
xBl [label="Bl: Barrelled", href="http://ncatlab.org/nlab/show/barrelled topological vector space"];
}

edge [style=invis];
yFD -> yHi;
yHi -> yNu;
yNu -> yBa;
yBa -> yIP;
yIP -> yMo;
yMo -> ySc;
ySc -> yUB;
yUB -> yFr;
yFr -> yZ1;

yDF -> yNo;
yNo -> yBo;
yBo -> yLF;
yLF -> yLB;
yLB -> yMe;
yMe -> yLC;
yLC -> yQC;
yQC -> yZ2;

yPt -> yBC;
yBC -> ySq;
ySq -> yCp;
yCp -> yRe;
yRe -> ySR;
ySR -> yQB;
yQB -> yMk;
yMk -> yBl;
yBl -> yZ3;


yFD -> xFD;
yHi -> xHi;
yNu -> xNu;
yBa -> xBa;
yIP -> xIP;
yMo -> xMo;
ySc -> xSc;
yUB -> xUB;
yFr -> xFr;
yDF -> xDF;
yNo -> xNo;
yBo -> xBo;
yLF -> xLF;
yLB -> xLB;
yMe -> xMe;
yLC -> xLC;
yQC -> xQC;
yPt -> xPt;
yBC -> xBC;
ySq -> xSq;
yCp -> xCp;
yRe -> xRe;
ySR -> xSR;
yQB -> xQB;
yMk -> xMk;
yBl -> xBl;




/*
FD -> Hi;
FD -> SC;
FD -> Nu;
FD -> Mo;
Hi -> Ba;
Hi -> IP;
Hi -> Re;
SC -> Me;
SC -> Se;
Mo -> Re;
Mo -> Pc;
Nu -> Sc;
Ba -> UB;
Ba -> Fr;
Ba -> DF;
Ba -> No;
IP -> No;
Re -> Bl;
Re -> SR;
UB -> Bo;
Fr -> Cn;
Fr -> Cp;
Fr -> Br;
Fr -> Me;
Cn -> Bo;
Cn -> LC;
Cp -> QC;
Br -> Bl;
Me -> Bo;
Me -> Pc;
SR -> QC;
Bo -> QB;
Bl -> QB;
QC -> Sq;
Pc -> Nm;
QB -> Mk;
Nm -> CP;
Sq -> LC;
LB -> LF;
LF -> Cp;
QCBo -> QC;
QCBo -> Bo;
QCBo -> Bl;
Hi -> AP;
Nu -> AP;
QCQB -> Bl;
QCQB -> QC;
Pt -> BC;
BC -> Cp;
Fr -> Pt;
Fr -> LF;
Ba -> LB;
*/
}

/*

/

Revised on May 27, 2010 10:49:03 by Andrew Stacey (80.203.115.53)