Vol. 103, No. 2, 1982

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Homeomorphic classification of certain inverse limit spaces with open bonding maps

William Thomas Watkins

Vol. 103 (1982), No. 2, 589–601

Let I = [0,1]. Let Nf be the N-th degree hat function from I to I. For example, 2f, 3f, and 4f are pictured below:

We are interested in classifying the spaces which are inverse limits of the unit interval using these bonding maps. In particular, for a fixed integer N 2, we are interested in classifying (up to homeomorphism) the space DN, which is lim
←−{I,Nf}. The main result of this paper is:

Theorem: DN is homeomorphic to DM if and only if M and N have the same prime factors.

Mathematical Subject Classification 2000
Primary: 54F50
Secondary: 54B25
Received: 2 September 1980
Revised: 21 January 1981
Published: 1 December 1982
William Thomas Watkins