Open covers, locally sectionable maps, sets of base points, and van Kampen's theorem
arXiv:1910.11620
Abstract
We generalize the van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of a space B are replaced by a locally sectionable map to B.
version 3, expanded proof, 16 pages