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homotopy groups of spheres builds on a great deal of background material, here briefly reviewed. Algebraic topology provides the larger context, itself built on topology and abstract algebra, with
homotopy groups as a basic example.. n-sphere. An ordinary sphere in three-dimensional space — the surface, not the solid ball — is just one example of what a sphere ... Formal classification. An ordered medium is defined as a region of space described by a function f(r) that assigns to every
point in the region an order parameter, and the possible values of the order parameter space constitute an order parameter space.The
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