20.1.2013 1:37, W. Dale Hall wrote: > Kaba wrote: >> Hi, >> >> In this page >> >> http://en.wikipedia.org/wiki/Indefinite_orthogonal_group >> >> there is the notation pi_0 in the topology section. What does it refer >> to? I don't see how the homotopy groups could cover n = 0... >> > Note that for two maps f,g : (S^0, *) --> (X,*) to b homotopic, there > must be a path connecting the images f(+1) and g(+1) of the non- > distinguished points in X. In short, the homotopy set of (X,*) is just > the set of path-components of X. In general, pi_0(X,*) has a > distinguished point consisting of the path-component of the point *.