I would like to make a further point about the topological fundamental groupoid of X. The information on this shows that iterating the fundamental groupoid does NOT lead to higher dimensional information on X. This was one of the facts leading to the Brown-Higgins construction of the homotopy double groupoid \rho(X,X_1,X_0) , where X_0 \subset X_1 \subset X, which in dimension 2 consists of homotopy classes rel vertices of maps of I^2 into X which take the edges of I^2 into X_1 and the vertices into X_0. This does inherit the obvious compositions of squares in two directions to become a strict double groupoid, and with which one can prove a 2-d van Kampen theorem. This was done in 1974, and published in 1978, in the teeth of opposition, which possibly explains why the new nonabelian calculations which resulted have not been generally recognised or taken up. Ronnie Brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]