Lifting Paths on Quotient Spaces
Nipissing University, North Bay, Ontario, Canada
Coauthors: D. Daniel (Lamar University), J. Nikiel (American U. of Beirut), L. B. Treybig (Texas A&M Univ.), E.D. Tymcahtyn (Univ. of Saskatchewan)
Let X be a continuum and G an upper semi-continuous decomposition of X such that each element of G is the continuous image of an (possibly non-metric) arc. If the quotient space X/G is the continuous image of an arc, under what conditions is X also the continuous image of an arc? Examples around the (non-metric) Hahn-Mazurkiewicz Theorem show that one must place severe conditions on G if one wishes to obtain positive results. Daniel (1998) solved the problem in the case that G has only one non-degenerate element. We consider the more general case in which the elements of G form a null family. We give a number of sufficient conditions and indicate with examples from the literature why those conditions are necessary.
Date received: March 14, 2004
Copyright © 2004 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # camc-94.