The big fundamental group, big Hawaiian earrings, and the big free groups
In this second of a series of three papers, the `big fundamental group' of a topological space is defined and studied. This big fundamental group is based on maps of big intervals (compact totally ordered connected spaces) rather than the usual unit interval, replacing also homotopy by big homotopy. Then the big Hawaiian earrings are defined as the one-point compactification of an arbitrary number of disjoint open intervals (the classical case corresponding to a countable number of such intervals), and it is shown that the big fundamental group of the big Hawaiian earrings is a big free group in the sense of the paper of the previous review (which is the first of the series; in the third one the fundamental groups of more general one-dimensional spaces will be studied).
scientific article; zbMATH DE number 1506030