Abstract
LetSndenote the sphere of all points in Euclidean space Rn+ 1at a distance of 1 from the origin andDn+ 1the ball of all points inRn+ 1at a distance not exceeding 1 from the origin The spaceXis said to beasphericalif for everyn≧ 2 and every continuous mapping:f:Sn→X, there exists a continuous mappingg:Dn+ 1→Xwith restriction to the subspaceSnequal tof. Thus, the only homotopy group ofXwhich might be non-zero is the fundamental group τ1(X, *) ≅G. IfXis also a cell-complex, it is called aK(G, 1). IfXandYareK(G, l)'s, then they have the same homotopy type, and consequently
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