High Quality Content by WIKIPEDIA articles! Given a size pair (M,f) where M is a manifold of dimension n and f is an arbitrary real continuous function defined on it, the i -th size functor[1], with i=0,ldots,n , denoted by F_i , is the functor in Fun(mathrm{Rord},mathrm{Ab}) , where mathrm{Rord} is the category of ordered real numbers, and mathrm{Ab} is the category of Abelian groups, defined in the following way. For xle y , setting M_x={pin M:f(p)le x} , M_y={pin M:f(p)le y} , j_{xy} equal to the inclusion from M_x into M_y , and k_{xy} equal to the morphism in mathrm{Rord} from x to y .

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