Symplectic Topologies ∑ Incepta Physica Mathematica

Symplectic Topologies ∑ Incepta Physica Mathematica scroll down

Finger Tip Topologies
Σ
Hans Tilgner

🧾 𝔄𝔟𝔰𝔱𝔯𝔞𝔠𝔱

We sugguest to develop a series of finger tip topologies, generalising the concept of metric, to area, volume, ... .
Examples are taken from short exact sequences in some categories of algebra like groups, algebras, ... and from symplectic vector spaces.
If it is possible to find axioms for areas, like those for metrics, it should be possible to find axioms for volume such that there are vector spaces with volume.
We expect examples from determinants and from pseudo-orthogonal vector spaces, where the topmost one-dimensional vector space in the exterior and Clifford-algebra has such a volume-structure. The special linear groups are their automorphism groups and the traceless linear Lie algebras are their derivation Lie algebras.

𝔍ncepta 𝔓hysica 𝔐athematica

_⮛_

↻ Archäologie ∴ Megalithkultur Havelquelle ↺

☎ UTF-codes

first published
24. May 2002

revised upload

Metric	Look at the concept of a metric in elementary topology: For a set 𝕄 a metric is a real-valued map 𝕄 × 𝕄 ——➤ ℝ , fulfilling the three axioms reflexivity, symmetry and the triangle unequality. But, there is missing something, the concept is not complete, something has been overlooked by the mathematician's community: Stop here and remember, how a metric leads to a topology on 𝕄, using systems of neighborhoods. Still no idea? ... Rethink ... there is a concept in which metric is only the first of a series of topological concepts, the best notion of which would be finger tip topologies. Still no idea? ...	ℝ are the real numbers
Metric- Area- Volume- ⋮ Topologies	Well – an area is a map 𝕄 × 𝕄 × 𝕄 ——➤ ℝ , fulfilling the four (?) axioms: Skew symmetry against permutation of adjacent entries, Jacobi identity, the tetraeder inequality and one (?) more axiom. To define a neighborhood one needs to construct the concept of a point of gravity, around which one can whirl a triangle of given area. The consecutive finger tip topology on 𝕄 in this line of argumentation is given by a volume-map 𝕄 × 𝕄 × 𝕄 × 𝕄 ——➤ ℝ , subject to five (?) axioms. Thus the category of topological spaces contains also area-, volume-, ... spaces besides the metric ones.	the map
Short Exact Sequences Lie Groups Lie Algebras	Examples of this area-concept should be given by symplectic manifolds, especially symplectic vector spaces, i.e. pairs of a set 𝕄 and a skew map resp. bilinear form 𝕄 × 𝕄 ——➤ ℝ , the area being constructed in terms of the symplectic form. This topologises 𝕄 entirely in terms of the symplectic form and the area. Other examples should come from the 2nd cohomology of groups ( and some more algebraic categories ), i.e. short exact sequences 𝔽 ➤——➤ 𝔾 ——➤➤ 𝕊 of groups, where there exists a pair of maps Σ and Δ, fulfilling two axioms. There are two well-known special cases, the retract case, in which the left arrow has a commuting inverted one, and the split case, in which the right arrow has a commuting inverted one — in group-theoretical language retract- and semi-direct products or equivalently -short exact sequences. When both come together we get a direct product. In the split case there is a skew map 𝕊 × 𝕊 ——➤ 𝔽 , usually called σ, which in the case of symplectic vector spaces is the symplectic bilinear form. In this case the resulting group 𝔾 is the Heisenberg group of quantum mechanics and the second example of an area map coincides with the first one.	𝔽 𝔾 𝕊 are groups and even symmetric spaces if the latter have a 2nd cohomology and short exact sequences
2nd Cohomology	It would be nice to show that for all short exact sequences the third group 𝕊 carries an area map, constructed in terms of Σ and Δ . In case the group is a Lie group, there is a 2nd cohomology, carried over by the tangent functor to its Lie algebra and the same holds for symmetric spaces in the definition of O. Loos and their tangent structures. In the direct case clearly both arrows in this short exact sequence have inverted arrows such that there is a commutative diagram of two short exact sequences. In general these tangent structures are Lie triples. But in the physical case of space-time they even are Jordan algebras, well-known to the Artin school of mathematics. In both cases there should be induced area maps.	in many algebraic categories
	see any book on general and metric topology.	start / top


		Literature with commentswith [ links to publications] and [ conference books]
	➿
	[Bou]	N Bourbaki Algebra I Hermann, Paris [1970] ISBN 2 7056 5675 8 remains the standard information on universality in algebra and chap. III §6 in that on symmetric algebras.
	➿
	[Col]	G P Collins Die Lösung eines Jahrhundertproblems Spektrum der Wissenschaft Sep [2004] pp 86-94 translated from the Scientific American on results of Perelman for 3-dimensional spaces.
	➿
	[Fmk]	A F Fomenko Differential Geometry and Topology Consultants Bureau, NY [1987] translated from Russian with more references.
	➿
	[God]	C Godbillon Géometrie Différentielle et Mécanique Analytique Hermann, Paris [1969] defines Poisson brackets on p 125.
	➿
	[How]	R E Howe On the Role of the Heisenberg Group in Harmonic Analysis Bull. Am. Math. Soc 3 no 2 [1981] pp 821-843
	[How]	R E Howe Remarks on Classical Invariant Theory Trans. Am. Math. Soc 313 no 2 [1989] pp 539-570
	➿
	[Kch]	M Köcher The Minnesota Notes on Jordan Algebras and Their Applications Springer Lecture Notes in Mathematics 1710 [1999] His concept of mutations IV �2 still has to be included here.
	➿
	[Kow]	O Kowalski Partial Curvature Structures and Conformal Transformations J. Differential Geometry 8 [1973] pp 53-70
	➿
	[ Ku l ]	R S Kulkarni Curvature and Metric Annals of Mathematics 91 [1970] pp 311-331 follows, together with Katsumi Nomizu and Oldrich Kowalski, the curvature axioms Singer & Thorpe's.
	[K70]	R S Kulkarni Curvature Structures and Conformal Transformations J. Differential Geometry 4 [1970] pp 425-451
	➿
	[ Lic ]	A Lichnérowicz Ondes et Radiations Électromagnétique et Gravitationelles en Relativité Générale Annali di Matematica Pura & Appl. 4 [1960] pp 1-95 is a very elegant representation of the concept, although written in the old-fashioned index notation. We rate this work as t h e major contribution to gravitational radiation end even to general relativity after Einatein !
	➿
	[Loo]	O Loos Symmetric Spaces I + II Benjamin N.Y. [1969] no ISBN We only use the first volume. We generalize his symmetric multiplication from hyperboloids (spheres) to arbitrary elements outside null-cones, this being well-known to the Artin school of mathematics, and this in turn to the complex case of pseudo-Hilbert spaces. One of the main points, following from Loos' definition of a symmetric space, is that instead of studying ℂℂ-algebras -in quantum mechanics - one should study algebras with an involution ( instead of the -anti-involution ).
	[L&N]	O Loos, E Neher Reflection Systems and Partial Root Systems Forum Math 23 [2011] pp 349-411 see also O Loos, E Neher Locally Finite Root Systems Mem Am Math Soc 171 n°811 [2004] pp 1-214
	➿
	[Nom] [KOT]	K Nomizu The Decomposition of Generalized Curvature Tensor Fields pp 335-345 in S Kobayash, M Obata, T Takahashi (ed.) Differential Geometry in Honor of Kentaro Yano Kinukuniya, Tokyo [1972] not online and no ISBN.
	➿
	[Poi]	H Poincaré Sur la Dynamique de l'Électron Comptes Rendus de l'Académie de France [1905] pp 1504-1508 first launched the concept of gravitational waves in the framework of special relativity only, however.
	➿
	[Pos]	E J Post Formal Structure of Electromagnetics North Holland, Amsterdam [1962] no ISBN is an inspiring book, though written in an old-fashioned way with indices: The electromagnetic constituency 4-tensor between the 2-tensors (4×4 matrices) of field-strengths and -intensities has the same symmetries as a curvature tensor.
	➿
	[Seg]	I Segal A variant of Special Relativity Pergamon, N.Y. [1969] no ISBN did first have this idea on a aariant between special and general relativity. Together with Loos' concept of loacally symmetric spaces this should lead to a quantization of general relativity.
	➿
	[S&T] [ S&I ]	M Singer, J A Thorpe The Curvature of 4-Dimensional Einstein Spaces pp 355-366 in D C Spencer, S Iyanaga (ed.) Global Analysis : Papers in Honor of K Kodaira Princeton University Press, Princeton N.J. [1969] no ISBN is the basic work to formulate general relativity in a modern mathematical language.
	➿
	[Sou]	J-M Souriau Structure des Systèmes Dynamiques Dunod, Paris [1970] no ISBN remains the classic book uniting theoretical physics and modern mathematics. There is an english translation:
	[Sou]	J-M Souriau Structure of Dynamical Systems Birkhäuser, Basel [1997] ISBN 0 8176 3695 1 defines the basis-free Poisson bracket on p 88.
	➿
	[Til]	H Tilgner A Class of Solvable Lie Groups and Their Relation to the Canonical Formalism Ann. Inst. H. Poincaré Sec. A Physique Théorique 13 no 2 [1972] pp 103-127
	[T77]	H Tilgner Graded Generalization of Weyl and Clifford Algebras J. Pure Appl. Algebra 10 no 2 [1977] pp 163-168
	[T78]	H Tilgner The Group Structure of Pseudo-Riemannian Curvature Spaces J.Math.Phys. 19 [1978] pp 1118-1125 shows how elegantly in- resp. covariance groups can be chased around Singer & Thorpe's curvature diagrams.
	[T84]	H Tilgner Conformal Orbits of Electromagnetic Riemannian Curvature Tensors – Electromagnetic Implies Gravitational Radiation pp 317-339 in Springer Lecture Notes in Mathematics 1156 [1984] ISBN 0 387 15994 0 has more details and references on the mathematical description of electromagnetic and gravitational radiation.

try browsers

⟨ ≡ 〈 ≡ x2329 ≡ 〈 ≡ 9001 ≡ lang || ⟩ ≡ 〉 ≡ x232A ≡ 〉 ≡ 9002 ≡ rang || ⟨,⟩ ≡ lang,rang
➥ ≡ 10149 || ⓣ ≡ 9443 || ∂ ≡ 8706
  ◊ ≡ loz || ⋄ ≡ 8900 || ♦ ≡ diams ≡ 9830 || ▰ ≡ 9648 || ▱ ≡ 9649
aber ⊟ ≡ 8863 als Index ist das beste Zeichen für eine Lie algebra neben −


ḑ ≡ 7697	ઠ ≡ 2720	ծ ≡ 1390	ð ≡ eth	δ ≡ delta	Ꮄ ≡ 5044	Ẍ ≡ 7820	Ẋ ≡ 7818	☓ ≡ 9747
ɂ ≡ 578	ɖ ≡ 598	⨆ ≡ 10758	⨳ ≡ 10803	𐰫 ≡ 66651	𐰪 ≡ 68650	𐡒 ≡ 67666	𐦰 ≡ 68016	⦚≡10650
Lichtkegl
ă ≡ 259	ᾰ ≡ 8112	ӑ ≡ 1233	&#..; ≡ b ?	č ≡ 269	ě ≡ 283	ğ ≡ 287	ǧ ≡ 487	ȟ ≡ 543
ĭ ≡ 301	ǐ ≡ 464	ῐ ≡ 8144	ǰ ≡ 496	ǩ ≡ 489	ň ≡ 328	ŏ ≡ 335	ř ≡ 345	š ≡ 353
š ≡ 154	ž ≡ 158	ĕ ≡ 277	&#...; ≡ ...
Serie:	ǎ ≡ 462	ǐ ≡ 464	ǒ ≡ 466	ǔ ≡ 468	ŭ ≡ 365	ǔ ≡ 468	ῠ ≡ 8160	ž ≡ 382
Inneres	Vorwärts	Lichtkegel
ȧ ≡ 551	ḃ ≡ 7683	ċ ≡ 267	ḋ ≡ 7691	ė ≡ 279	ḟ ≡ 7711	ġ ≡ 289
ḣ ≡ 7715	ṁ ≡ 7745	ȯ ≡ 559	ṗ ≡ 7767	ṙ ≡ 7769	ṡ ≡ 7777	ṫ ≡ 7787
ù ≡ 249 ?	&#; ≡ v ?;	ẇ ≡ 7815	ẋ ≡ 7819	ẏ ≡ 7823	ż ≡ 380
rückwärts
ạ ≡ 7841	ᾳ ≡ 8115	ḅ ≡ 7685	ḍ ≡ 7693	ẹ ≡ 7865	ḥ ≡ 7717	ị ≡ 7883	ḳ ≡ 7731
ḷ ≡ 7735	ṃ ≡ 7747	ṇ ≡ 7751	ọ ≡ 7885	ṛ ≡ 7771	ṣ ≡ 7779	ṭ ≡ 7789	ș ≡ 537	ţ ≡ 355
ụ ≡ 7909	ṿ ≡ 7807	ẉ ≡ 7817	ỵ ≡ 7925	ẓ ≡ 7827
LangVokal
ā=ā ≡ 257 amacr	ᾱ ≡ 8113≠ alphamacr	ē=ē ≡ 275 emacr	ī ≡ 299 ī≡imacr	ῑ ≡ 8145	ō ≡ 333 ō≡omacr	ū ≡ 363 ū≡umacr	Τ ≡ 832 ≠ &lmacr;	ȳ≡ 563 ≠&ymacr;
Konsonant	ebenso
ḡ ≡ 7713 ≠&gmacr;
oder auch
ḇ ≡ 7687	ḏ ≡ 7695	ǥ ≡ 485	ẖ ≡ 7830	ḵ ≡ 7733	ḻ ≡ 7739 ≠&lmicr;	ṉ ≡ 7753 ≠&nmicr;	ṟ ≡ 7775	ṯ ≡ 7791
ẕ ≡ 7829
.
SondrZei
‘ ≡ lsquo	’ ≡ rsquo	⣏ ≡ 10447	⣹ ≡ 10489	⣏x⣿y⣹	⢎ ≡ 10382	⡱ ≡ 10353	⢎⢸⡇⡱	᠞ ≡ 6174
.
≺≡8826	≻≡8827	₪≡8362	⊞≡8862	■≡9632	∎≡8718	▣≡9635	ѻ≡1147	𝕄 ≡ Mopf
.
ɑ≡593	ℒ≡8466	ℓ≡8467	ℎ≡8462	ℯ≡8495	ℴ≡8500	ɡ≡609	ℊ≡8458	፪≡4970
ᦔ≡6548	ℐ≡8464	ℑ≡8465	Ƥ≡420	Ꮤ≡5076	၂≡4162	Ĵ≡308	ʝ≡669	፫≡4971
ᚹ≡5817	ᚸ≡6816	ឋ≡6027	˟≡735	ᚸ≡5816	ᳲ≡7410	⪤≡10916	⩆≡10822	♉≡9801
ʤ ≡ 676	ǳ ≡ 499	ẟ ≡ 7839	⸹ ≡ 11833	⸎ ≡ 11790	⭍ ≡ 11085	ㄅ ≡ 12549	⻈ ≡ 11976	〜 ≡ 12316
⪥ ≡ 10917	⤫ ≡ 10539	⤬ ≡ 10540	✕ ≡ 10005	⸎ ≡ 10006	ᛤ ≡ 5860	❎ ≡ 10062	⦄ ≡ 10628	⦅ ≡ 10629
↱≡8625	↲≡8626	╠≡9568	╣≡9571	Ⅼ≡8556	—≡8212	―≡8213	‖≡8214	∣≡8739
.
&xcaron;≡ xcaron ˇ≡caron	&xbreve;≡ xbreve ˘≡breve	&xdot;≡ xdot ˙≡dot	&xogon;≡ xogon ˛≡ogon	&xstrok;≡ xstrok ≡&strok;	&xmacr; ≡xmacr ¯≡macr	𝓍≡xscr ℒ ≡Lscr &scr;≡scr	𝕍≡Vopf 𝔼≡Eopf 𝕥≡topf	&xcedil;≡ xcedil ¸≡cedil
.
&xtilde;≡ xtilde	&xacute;≡ xacute	&xgrave;≡ xgrave	&xdblac;≡ xdblac	&xuml;≡ xuml	◯≡ xcirc	&xring;≡ xring	𝕤≡ sopf	&xmath;≡ xmath
.
&xelig;≡ xelig	&xlig;≡ xlig	&xgreen;≡ xgreen	&xslash;≡ xslash	&xmidot;≡ xmidot	&xnodot;≡ xnodot	&xnof;≡ xnof	𝕩≡ xopf	ƒ≡ fnof
.
ˆ≡ circ	¸≡ cedil	&green;≡ green	&slash;≡ slash	&midot;≡ midot	&nodot;≡ nodot	&nof;≡ nof	&opf;≡ opf	&lig;≡ lig
.
{≡lcub	}≡rcub	>>≡gt GT	¦≡ brvbar	·≡ middot	·≡ centerdot	•≡ bull	«≡ laquo	&sub1;≡ sub1
.
܅≡1797	ˍ≡717	˅≡709	̌≡780	ˇ≡711	῏≡8143	Ⴭ≡4301	╣x║y╠	╣x╏y╠
.
ℓíℯ(.) gut 𝓁𝒾ℯ	ί	ℓ℩ℯ(.)	ℓιℯ(.) jota ℓ𝒾ℯ𝔾 𝕝𝕚𝕖𝔾	ℓíℯ(.) 𝕝ie𝔾	ss p( , ) 𝕊pℙ 𝕤𝕡p	∋≡8715	℈≡8456	સ≡2744
.
⭮ ≡ 11118	⤾ ≡ 10558	⮨ ≡ 11176	⌣ ≡ 8995	‿ ≡ 8255	⏝ ≡ 9181	⊔ ≡ 8852	␧ ≡ 9255	⌴⌴≡ 9012
᚜ ≡ 5788	᚛ ≡ 5787	ᛃ ≡ 5827	ℓ ≡ 8467	Ῐ ≡ 8152	Ĭ ≡ 300	Ꭻ ≡ 5035	⛌ ≡ 9932	※ ≡ 8251
፠ ≡ 4960	የ ≡ 4840	፻ ≡ 4987	Ꮲ ≡ P 5090	🩀 ≡ 129600	🪤 ≡ 127000	🦨 ≡ 129448	🐀 ≡ 128000	🟨 ≡ 129000
🦧 ≡ 129447	🦨 ≡/ 129448 &skunk;	🦩 ≡ 129449	🦪 ≡ 129450	🦫 ≡ 129451 &Ape;	🦬 ≡ 129452 &pen;	🕮 ≡/ 128366 &Book;	🦮 ≡/ 129454 &dog;	🦯 ≡ 129455
🦰 ≡ 129456	🦱 ≡ 129457	🦲 ≡ 129458	🦳 ≡ 129459	🦴 ≡ 129460	🦵 ≡ 129461	🦶 ≡ 129462	🦷 ≡ 129463	🦸 ≡ 129464
🦹 ≡ 129465	🦺 ≡ 129466	🦻 ≡ 129467	🦼 ≡ 129468	🦽 ≡ 129469	🦾 ≡ 129470	🦿 ≡ 129471	🧀 ≡ 129472	🧁 ≡ 129473
🧂 ≡ 129474	🧃 ≡ 129475	🧄 ≡ 129476	🧅 ≡ 129477	🧆 ≡ 129478	🧇 ≡ 129479	🧈 ≡ 129480	🧉 ≡ 129481	🧊 ≡ 129482
🧋 ≡ 129483	🧌 ≡ 129484	🧍 ≡ 129485	🧎 ≡ 129486	🧏 ≡ 129487	🧐 ≡ 129488	🧑 ≡ 129489	🧒 ≡ 129490	🧓 ≡ 129491
🧔 ≡ 129492	🧕 ≡ 129493	🧖 ≡ 129494	🧗 ≡ 129495	🧘 ≡ 129496	🧙 ≡ 129497	🧚 ≡ 129498	🧛 ≡ 129499	🧜 ≡ 129500
🧝 ≡ 129501	🧞 ≡ 12502	🧟 ≡ 129503	🧠 ≡ 129504	🧡 ≡ 129505	🧢 ≡ 129506	🧣 ≡ 129507	🧤 ≡ 129508	🧥 ≡ 129509
🧦 ≡ 129510	🧧 ≡ 129511	🧨 ≡ 129512	🧩 ≡ 129513	🧪 ≡ 129514	🧫 ≡ 129515	🧬 ≡ 129516	🧭 ≡ 129517	🧮 ≡ 129518
🧯 ≡ 129519	🧰 ≡ 129520	🧱 ≡ 129521	🧲 ≡ 129522	🧳 ≡ 129523	🧴 ≡ 129524	🧵 ≡ 129525	🧶 ≡ 129526	🧷 ≡ 129527
🧸 ≡ 129528	🧹 ≡ 129529	🧺 ≡ 129530	🧻 ≡ 129531	🧼 ≡ 129532	🧽 ≡ 129533	🧾 ≡ 129534	🧿 ≡ 129535	ℭ𝔓_x^u𝔗
ᑭ ≡ 5229	ᱞ ≡ 7262	𐡒 ≡ 67666	૭ ≡ 2797	ᱧ ≡ 7271	ᱬ ≡ 7276	ᱽ ≡ 7293	ᵱ ≡ 7537	␠ ≡ 9248
Ῥ ≡ 8172	Ⲣ ≡ 11426	↯ ≡ 8623	⭍ ≡ 11085	⨇ ≡ 10759	⨈ ≡ 10760	Ⱎ ≡ 11294	⨰ ≡ 10800	⨉ ≡ 10761
Ⱀ ≡ 11280	Ᵽ ≡ 11363	⬶ ≡ 11062	⩔ ≡ 10836	⩕ ≡ 10837	⩖ ≡ 10838	Ⱎ ≡ 11294	⬬ ≡ 11052	⬭ ≡ 11053
Ⲭ ≡ 11436	㇣ ≡ 12771	ㄗ=P ≡ 12567	⼫ ≡ 12075	Ⱞ ≡ 11310	⩖ ≡ 10838	Ⱳ ≡ 11378	ⱳ ≡ 11379	ⱱ ≡ 11377
Ꮪ ≡ 5082=S	Ꮱ ≡ 5089	⚐ ≡ 9872	⚑ ≡ 9873	ᳱ ≡ 7409	ᘮ ≡ 5678	℧ ≡ 8487	ᙀ ≡ 5696	ប ≡ 6036
Ⴧ ≡ 4295	Ⴝ ≡ 4285	Տ ≡ 1359	⺋ ≡ 11915	⼰ ≡ 12080	⼐ ≡ 12048	ㄩ ≡ 12585	႗ ≡ 4247	ປ ≡ 3739
ၓ ≡ 4179	ಽ ≡ 3261	ჷ ≡ 4343	ჽ ≡ 4349	ᗉ ≡ 5577	ᗆ ≡ 5574	ⴝ ≡ 11549	ട ≡ 3359	Մ ≡ 1348
ઽ ≡ 2749	ऽ ≡ 2365	ડ ≡ 2721	ߎ ≡ 1998	ម ≡ 6040	ᘴ ≡ 5684	ᘢ ≡ 5666	ப ≡ 2986	য ≡ 2479
ꇙ ≡ 41433	𐍃 ≡ 66371	𐍊 ≡ 66378	ꂀ ≡ 41088	𐋇 ≡ 66247	כ ≡ 1499	၁ ≡ 4161	ι ≡ iota	𓍝 ≡ 61685
𐠔 ≡ 67604	𐠲 ≡ 67634	𐠴 ≡ 67636	𐠂 ≡ 67586	𐐕 ≡ 66581	𐐣 ≡ 66595	𐦰 ≡ 68016	⫖ ≡ 10966	𐩕 ≡ 68181
Ỻ ≡ 7930	Ꮤ ≡ 5076	ဝ ≡ 4125	လ ≡ 4124	ᔓ ≡ 5395	ᔔ ≡ 5396	⮤⮥ ⭦⭧ ↰_↱ ⮬⮭	ᄽ ≡ 4413	Ⴘ ≡ 4280
≺\| ≡ 8826	\|≻ ≡ 8827	⊀\| ≡ 8832	\|⊁ ≡ 8833	⟪ ≡ 10218	⟫ ≡ 10219	⮲_⮳ ⭦⭧ ↰_↱ ⮬⮭	ℝ ≡ 8477	ℤ ≡ 8484
⨇ ≡ 10759	⨈ ≡ 10760	Ⳙ ≡ 11480	⨆ ≡ 10758	ℂ ≡ 8450	ℍ ≡ 8461	ℙ ≡ 8473	ℚ ≡ 8474	ℕ ≡ 8469
⦓ ≡ 10643	⦔ ≡ 10644	⦕ ≡ 10645	⦖ ≡ 10646	⪻ ≡ 10939	⪼ ≡ 10940	⩽ ≡ 10877	⩾ ≡ 10878	⫹ ≡ 11001
ᖘæ(G) ∘ ○	ᖘæ(G)	∘ ≡ 8728	○ ≡ 9675	◌ ≡ 9676	° ≡ 176	º ≡ 186	œ	æᒼ
Ԗ> ≡ 1302	Ƿ ≡ 503	œ ≡ 156	Ҏ ≡ 1166	ᖘ ≡ 5528	₱ ≡ 8369	⁋ ≡ 8267	∐ ≠ ⭮ 8720	℗ ≡ 8471
ⅽ ≡ 8573	င≡4100	ᒼ ≡ 5308	ᄃ≡4355	ᆮ≡4526	ເ ≡ 3776	ᛃ ≡ 5827	ᣞ ≡ 6366	᠞ ≡ 6174
⊔︀ ≠ ⭮ sqcups	⊔ sqcup	𝕍≡Vopf	𝒱≡Vscr	𝕄≡Mopf	ℳ≡Mscr	☎ ≡ phone	𝔼 ≡ Eopf	𝕃 ≡ Lopf
&book; ≡ book	&books; books	𝔻≡Dopf	𝒯≡Tscr	ℕ≡Nopf	𝒪≡Oscr	𝔹 ≡ Bopf	ℂ ≡ Copf	𝕎 ≡ Wopf
&click; ≡ click	&view; view	&page;≡ page	&clear;≡ clear	&cl;≡ cl	&vw;≡ vw	&bk; ≡bk	&pg; ≡ pg	&pag; ≡ pag
&bell; ≡ bell	&Bell; Bell	☾≡9790	☽≡9789	◖≡9686	◗≡9687	◀≡9664	▶ ≡9564	⌰ ≡9008
𫝏 ≡ 177999	𮊫 189099	𰦻≡ 190999	𫙱≡ 177777	𫝐≡ 178000	𭹠≡ 188000	𭻏≡ 1881111	𭼾 ≡ 188222	𮀜 ≡ 188444
.
〈≡9001	〉≡9002	❮≡10094	❯≡10095	≮≡8814	≯≡8815	&see;≡ see	&look; ≡ look	≝ ≡8797 ≠&def;
⫷≡10999	⫸≡11000	⦅≡10629	⦆≡10630	⮘≡11160	⮚≡11162	⮜≡11164	⮞ ≡11166	⪡⪢≡10913
⭮ ≡ ↻ ≠ ↻	⭯ ≡ ↺ ≠ ↺	š ≡ scaron	&ocaron;≡ ocaron	Ô≡ ocirc	𝒪 ≡ oscr	&Mtilde; ≡ Mtilde	ñ ≡ ntilde	𝕋 ≡ Topf

Buchstaben des arabischen Alphabet's
	NCR dez		arab	deutsch	[Spi]	[Stg]	[Whr]	[WBS]
Nr.	UTF-8	arab	phon	phon	Trans
1.	1575	ا	Alif	aa/.../	a	a	a	ɂ
2.	1576	ب	Baa	b/v	b	b	b	b
								p
3.	1578	ت	Thaa	t	t	t	t	t
4.	1579	ث	θaa	θ/t/s	s	s-	ṯ	θ
5.	1580	ج	Dschiim	g/j/dsch	g	j	ǧ	j	ݼ≡1916
								č
6.	1581	ح	Haa	hh	ḥ	ḥ	ḥ	ح
7.	1582	خ	Chaa	ch	ḫ	h••	ḫ	x	ݗ≡1879
8.	1583	د	Daal	d	d	d	d	d
9.	1584	ذ	Dhaal	th	z	ẓ	ḏ	ઠ
10.	1585	ر	Raa	r	rh	r	r	r
11.	1586	ز	Ssaai	ss	z	z	z	z
12.	1587	س	Siin	s	s	s	s	s
13.	1588	ش	Schiin	sch	ṥ	ś	š	š	ݽ≡1917
14.	1589	ص	Ssad	ss	ṣ	ṣ	ṣ	ṣ
15.	1590	ض	Daad	dd	ḍ	ḍ	ḍ	ઠ•
16.	1591	ط	Ttaa	tt	ṭ	ṭ	ṭ	ṭ
17.	1592	ظ	Zaa	zz	z	z-	ẓ
18.	1593	ع='=ˁ	'Ain	'	'	'	ˁ	ع
19.	1594	غ	Ghain	fr. r	ġ	g	ġ or ḡ	ġ
20.	1601	ف	Faa	f	f	f	f	f
21.	1602	ق	Kkaaf	kk	q	q	q	q
								g
22.	1603	ك	Kaaf	k	k	k	k	k
23.	1604	ل	Laam	l	l	l	l	l
24.	1605	م	Miim	m	m	m	m	m
25.	1606	ن	Nuun	n	n	n	n	n
26.	1607	ه	Haa	h	h	h	h	h
27.	1608	و	Waaw	uu/u/au	w/u/au	w	w	w
28.	1610	ي	Yaa	ii	y	y	y	y

häufig	1577	ة	+t,+a,+h	Ta	marbuta

top / start

5 more Links
↻in the Box↺

Suzanne Roman

webDesign
Suzanne Roman
Australia