Webvgl. 1.1 in Hatcher Alg. Top. W9 (24.04. und 28.04.) Provisorisch: Der Satz von Seifert und van Kampen: Motivation an einem einführenden Beispiel. Algebraeinschub: Das freie Produkt von Gruppen, die Universelle Eigenschaft des freien Produktes Der Satz von S-vK für offene Überdeckungen mit zwei Mengen, pi_1(S^n)=1 mit S-vK, Beispiel eines ...

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Web1.3. SIMPLICIAL COMPLEXES 7 De nition (2-simplex). Let v 0, v 1, and v 2 be three non-collinear points in Rn.Then ˙2 = f 0v 0 + 1v 1 + 2v 2 j 0 + 1 + 2 = 1 and 0 i 18i= 0;1;2g … Web1 Homotopy III Algebraic Topology So from the point of view of homotopy, the one-point space f0gis the same as Rn!So dimension, or even cardinality, is now a meaningless concept. pirch terms and conditions

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Web$\begingroup$ Re "weird example of a compact set": what you mean is probably a "quasicircle" (Hatcher, Alg Top, Sec 1.3, Ex 7), because the complement of the closure … Web$\begingroup$ Re "weird example of a compact set": what you mean is probably a "quasicircle" (Hatcher, Alg Top, Sec 1.3, Ex 7), because the complement of the closure of the graph of $\sin(1/x), x>0$ is clearly contractible. $\endgroup$ – Victor Protsak. Jun … Web1 INTRODUCTION 5 A map f: (I;@) !(X;x 0) is geometrically a path in Xparametrized by the unit interval I= [0;1] with starting point f(0) = x 0 and endpoint f(1) = x 0.Such maps are also called based loops. Similarly, a map f: (I2;@I2) !(X;x 0) is geometrically a membrane in X parametrized by the square I2, such that the boundary of the square maps to the base point pirch thermador