2002/04/10 by Brian Raines
Mathematics · #math.GN #msc:54H20 #msc:54F15 #msc:37E25
published as Proceedings of the Ninth Prague Topological Symposium, (Prague, 2001),pp. 253--263, Topology Atlas, Toronto, 2002 · 11 pages
arxiv created 2002/04/10 · arxiv updated 2009/11/30
In this paper we examine the topology of inverse limit spaces generated by maps of finite graphs. In particular we explore the way in which the structure of the orbits of the turning points affects the inverse limit. We show that if f has finitely many turning points each on a finite orbit then the inverse limit of f is determined by the number of elements in the ω-limit set of each turning point. We go on to identify the local structure of the inverse limit space at the points that correspond to points in the ω-limit set of f when the turning points of f are not necessarily on a finite orbit. This leads to a new result regarding inverse limits of maps of the interval.