A van Kampen theorem

AbstractThis paper contains a generalization of the Seifert-van Kampen Theorem to the case in which not all of the elements in the cover contain the basepoint. In particular, a condition on the cover is given which permits the definition of a fundamental group functor from the cover into the category of groups. The colimit of this functor is the fundamental group of X. The techniques used in this paper are similar to those used in [1], where the case of covers in which the intersection of three elements is void was considered