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About: Size homotopy group     Goto   Sponge   NotDistinct   Permalink

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The concept of size homotopy group is analogous in size theory of the classical concept of homotopy group. In order to give its definition, let us assume that a size pair is given, where is a closed manifold of class and is a continuous function. Consider the lexicographical order on defined by setting if and only if . For every set . In other words, the first size homotopy group of the size pair computed at and is the imageof the first homotopy group with base point of the topological space , when is the homomorphism induced by the inclusion of in .