Topicity - Homotopic

Homotopic

Homotopic groups in a chemical compound are equivalent groups. Two groups A and B are homotopic if the molecule remains the same (including stereochemically) when the groups are interchanged with the remaining parts of the molecule fixed. Homotopic atoms are always identical, in any environment. Homotopic NMR-active nuclei have the same chemical shift in an NMR spectrum. For example, the four hydrogen atoms of methane (CH4) are homotopic with one another, as are the two hydrogens or the two chlorines in dichloromethane (CH2Cl2).

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Other articles related to "homotopic":

Homotopy Equivalence - Null-homotopy
... A function f is said to be null-homotopic if it is homotopic to a constant function ... For example, a map from the circle S1 is null-homotopic precisely when it can be extended to a map of the disc D2 ... the identity map from X to itself—which is always a homotopy equivalence—is null-homotopic ...
Homotopy Category Of Chain Complexes
... complexes modulo homotopy" that is, we define an equivalence relation if f is homotopic to g and define to be the quotient by this relation ... if one notes that this is the same as taking the quotient by the subgroup of null-homotopic maps ... The name "homotopy" comes from the fact that homotopic maps of topological spaces induce homotopic (in the above sense) maps of singular chains ...
Homotopy - Formal Definition - Properties
... Continuous functions f and g are said to be homotopic if and only if there is a homotopy H taking f to g as described above ... Being homotopic is an equivalence relation on the set of all continuous functions from X to Y ... relation is compatible with function composition in the following sense if f1, g1 X → Y are homotopic, and f2, g2 Y → Z are homotopic, then their compositions f2 ∘ f1 and g2 ∘ g1 X ...
Contractible Space
... In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e ... if it is homotopic to some constant map ... the identity map is null-homotopic) ...