Homeomorphic classification of certain inverse limit spaces with open bonding maps

William Thomas Watkins

Vol. 103 (1982), No. 2, 589–601

DOI: 10.2140/pjm.1982.103.589

Abstract

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:

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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 D_N, which is {I,^Nf}. The main result of this paper is:

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

Mathematical Subject Classification 2000

Primary: 54F50

Secondary: 54B25

Milestones

Received: 2 September 1980

Revised: 21 January 1981

Published: 1 December 1982