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Enantiotopic groups are identical and indistinguishable except in chiral environments. For instance, the CH 2 hydrogens in ethanol (CH 3 CH 2 OH) are normally enantiotopic, but can be made different (diastereotopic) if combined with a chiral center, for instance by conversion to an ester of a chiral carboxylic acid such as lactic acid, or if coordinated to a chiral metal center, or if ...
Being homotopic is an equivalence relation on the set of all continuous functions from X to Y. This homotopy relation is compatible with function composition in the following sense: if f 1, g 1 : X → Y are homotopic, and f 2, g 2 : Y → Z are homotopic, then their compositions f 2 ∘ f 1 and g 2 ∘ g 1 : X → Z are also homotopic.
Two maps , are called homotopic relative to A if they are homotopic by a basepoint-preserving homotopy : [,] such that, for each p in and t in [,], the element (,) is in A. Note that ordinary homotopy groups are recovered for the special case in which A = { x 0 } {\displaystyle A=\{x_{0}\}} is the singleton containing the base point.
1 Homotopic groups vs Enantiotopic & Diastereotopic. 2 comments. Toggle the table of contents. Talk: Topicity. Add languages. Page contents not supported in other ...
In particular, a counterclockwise interchange by half a turn is not homotopic to a clockwise interchange by half a turn. Lastly, if M is R {\displaystyle \mathbb {R} } , then this homotopy class is empty.
Any two knots in 3-space are equivalent by regular homotopy, though not by isotopy. This curve has total curvature 6π, and turning number 3.. The Whitney–Graustein theorem classifies the regular homotopy classes of a circle into the plane; two immersions are regularly homotopic if and only if they have the same turning number – equivalently, total curvature; equivalently, if and only if ...
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The null homotopic class acts as the identity of the group addition, and for X equal to S n (for positive n) — the homotopy groups of spheres — the groups are abelian and finitely generated. If for some i all maps are null homotopic, then the group π i consists of one element, and is called the trivial group.