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Size Homotopy Group
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High Quality Content by WIKIPEDIA articles! 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 (M,varphi) is given, where M is a closed manifold of class C^0 and varphi:Mto mathbb{R}^k is a continuous function. Let us consider the partial order preceq in mathbb{R}^k defined by setting (x1,ldots,xk)preceq(y1,ldots,yk) if and only if x1 le y1,ldots, xk le yk . For every Yinmathbb{R}^k we set M{Y}={Zinmathbb{R}^k:Zpreceq Y} . Assume that Pin MX and Xpreceq Y . If alpha , beta are two paths from P to P and a homotopy from alpha to beta , based at P , exists in the topological space M{Y} , then we write alpha approx{Y}beta . The first size homotopy group of the size pair (M,varphi) computed at (X,Y) is defined to be the quotient set of the set of all paths from P to P in MX with respect to the equivalence relation approx{Y} , endowed with the operation induced by the usual composition of based loops.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131193200
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131193200
- Format Fachbuch
- Titel Size Homotopy Group
- Herausgeber Betascript Publishing
- Anzahl Seiten 80
- Genre Mathematik
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