Big fundamental groups: generalizing homotopy and big homotopy (Q272838)

The notion of the big fundamental group was introduced in [\textit{J.W. Cannon} and \textit{G.R. Conner}, Topology Appl. 106, No. 3, 273--291 (2000; Zbl 0955.57003)]. The idea is to generalize the standard fundamental group by extending the domain of topological loops: instead of the unit interval (or the circle) the domain of a big loop is a big interval, i.e., any compact totally ordered connected space. This definition is well suited to non-second countable spaces in which the standard fundamental group may prove to be too weak an invariant. However, it turns out that the generalization of the corresponding theory and constructions contains a number of technical details.NEWLINENEWLINEIn this paper the author proves that the big fundamental group may be defined for any pointed space \(X\). Given such a space he provides a cardinal, for which the corresponding big interval may be used to realize any big loop in \(X\).