Closed mappings which lower dimension
Open and closed mappings and compactification
Compactification and the continuum hypothesis
On the Whitehead Theorem in shape theory
Closed mappings and local dimension
Attractors and Inverse Limits.
This paper surveys some recent results concerning inverse limits of tent maps. The survey concentrates on Ingram’s Conjecture. Some motivation is given for the study of such inverse limits.
An example concerning the Whitehead Theorem in shape theory
On the classification of inverse limits of tent maps
Let and be tent maps on the unit interval. In this paper we give a new proof of the fact that if the critical points of and are periodic and the inverse limit spaces and are homeomorphic, then s = t. This theorem was first proved by Kailhofer. The new proof in this paper simplifies the proof of Kailhofer. Using the techniques of the paper we are also able to identify certain isotopies between homeomorphisms on the inverse limit space.
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