Modern differential geometry for physicists 2nd ed , c isham

... metric spaces. For example, let C( [a, b ], R) denote the space of all real-valued, continuous functions on the closed interval [a, b] := { T E R 1 a 5 T 5 b }. A metric can ... the specific metric function, d, involved. 2. If Eq. (1.2.7) is replaced by the weaker condition “d(z,y) 2 0, with d(z,z) = 0 for all z E X” (ie ., there may be z # y such that ... topological differences between, for example, a 2-sphere, a 2-torus and a 1264- sphere are coded entirely in their respective distance functions, all of which could be considered to be...

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