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  • A '''manifold''' is a [[topological space]] locally [[homeomorphic]] to an [[open set | open]] [[ball]] in some [[Euclidean space]]. Informal
    2 KB (237 words) - 20:08, 13 October 2019
  • ...ct ''n'' manifold is homotopy equivalent to the ''n'' sphere [[iff]] it is homeomorphic to the ''n'' sphere, or, more simply, that only a ''n'' manifold with no ho ...Every [[simply connected]], compact three-manifold (without boundary) is [[homeomorphic]] to the three-sphere."
    13 KB (1,969 words) - 16:57, 22 February 2024
  • ...ecifically, if <math>X</math> and <math>Y</math> are [[homeomorphic spaces|homeomorphic]] then <math>\pi_1(X)</math> and <math>\pi_1(Y)</math> are isomorphic. ...h> (where <math>S^n</math> is the [[n-sphere]]), and hence a circle is not homeomorphic to a sphere.
    8 KB (1,518 words) - 19:11, 23 January 2017
  • ...d as "Every simply connected, compact three-manifold (without boundary) is homeomorphic to the three-sphere."
    690 bytes (107 words) - 14:12, 31 March 2017
  • ...every closed topological three-dimensional [[manifold]] is [[homeomorphism|homeomorphic]] to a [[hypersphere|3-sphere]]. ...d as "Every simply connected, compact three-manifold (without boundary) is homeomorphic to the three-sphere."
    929 bytes (138 words) - 20:44, 29 September 2024
  • A knot is an embedding of S^1 (the circle) into R^3. Every knot is homeomorphic to S^1.
    373 bytes (53 words) - 15:59, 16 December 2024