Topology Atlas
Document # ppae-24

## Orbits of turning points for maps of finite graphs and inverse limit spaces

### Brian Raines

Proceedings of the Ninth Prague Topological Symposium
(2001)
pp. 253-263
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 \omega-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 \omega-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.

Mathematics Subject Classification. 54H20 54F15 37E25.

Keywords. inverse limits, graph, continuum.

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Copyright © 2002
Charles University and
Topology Atlas.
Published April 2002.