About: Solenoid (mathematics)

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In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms where each is a circle and fi is the map that uniformly wraps the circle for times around the circle . This construction can be carried out geometrically in the three-dimensional Euclidean space R3. A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group.

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rdfs:label	Solenoid (Mathematik) (de) Solénoïde (mathématiques) (fr) Solenoïde (wiskunde) (nl) Solenoid (mathematics) (en)
rdfs:comment	In der Mathematik sind Solenoide gewisse Kontinua, die unter anderem als Attraktoren in der Theorie der dynamischen Systeme vorkommen. (de) In mathematics, a solenoid is a compact connected topological space (i.e. a continuum) that may be obtained as the inverse limit of an inverse system of topological groups and continuous homomorphisms where each is a circle and fi is the map that uniformly wraps the circle for times around the circle . This construction can be carried out geometrically in the three-dimensional Euclidean space R3. A solenoid is a one-dimensional homogeneous indecomposable continuum that has the structure of a compact topological group. (en) En mathématiques, pour un nombre premier donné p, le solénoïde p-adique est le groupe topologique défini comme la limite projective du système où i parcourt les entiers naturels, et chaque Si est un cercle, et qi enroule le cercle p fois autour du cercle . (fr) In de algebraïsche topologie, een deelgebied van de wiskunde, is een solenoïde een compacte aaneengesloten topologische ruimte (dat wil zeggen een ) dat kan worden verkregen als de van een invers systeem van topologische groepen en continue homomorfismen. (Si, fi), fi: Si+1 → Si, i ≥ 0, waar elke Si een cirkel is en fi de afbeelding is die de cirkel Si+1 op uniforme wijze ni keer (ni ≥ 2) rond de cirkel Si wikkelt (Engels: "wrapt"). (nl)
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dcterms:subject	Ring theory Continuum theory Topological groups Algebraic topology Number theory P-adic numbers
Wikipage page ID	2217712 (xsd:integer)
Wikipage revision ID	1093867428 (xsd:integer)
Link from a Wikipage to another Wikipage	Metrizable space Topological dimension Topologically transitive David van Dantzig Homeomorphic Homomorphism Pathological (mathematics) Dynamical system Bucket-handle Ring theory Compact space Continuous function Mathematics Solid torus Circle Branched manifold Connected space Continuum (topology) Profinite integer Leopold Vietoris Long exact sequence Stephen Smale Continuum theory Embedding Path connected Topological groups Topological group Algebraic topology Number theory Euclidean space Foliation P-adic number Simplicial complex Symbolic dynamics P-adic numbers Attractor Inverse limit Hyperbolic set Toroidal and poloidal coordinates Bulletin of the AMS Pontryagin duality Cantor set Solenoid Čech cohomology Locally connected Euclidean topology Immersion (mathematics) Stable manifold Periodic point Topological space Protorus Unit disk Steenrod Hyperbolic dynamics Dense subset Homology theories
Link from a Wikipage to an external page	http://www.numdam.org/item%3Fid=PMIHES_1974__43__169_0 http://www.ams.org/bull/1967-73-06/S0002-9904-1967-11798-1/S0002-9904-1967-11798-1.pdf
sameAs	Solenoid (mathematics) Solenoid (mathematics) Solenoid (mathematics) Solenoid (mathematics) Solenoid (mathematics) Solenoid (mathematics) Solenoid (mathematics)
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