The Big Fundamental Group, Big Hawaiian Earrings, and the Big Free Groups

In this second paper in a series of three we generalize the notions of fundamental group and Hawaiian earring . In the first paper [CC1] we generalized the notion of free group to that of a big free group. In the current article we generalize the notion of fundamental group by defining the big fundamental group of a topological space. We also describe big Hawaiian earrings, which are generalizations of the classical Hawaiian earring. We then prove that the big fundamental group of a big Hawaiian earring is a big free group.