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 {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.
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