Vol. 50, No. 1, 1974

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Homeomorphisms of manifolds with zero-dimensional sets of nonwandering points

Lawrence Stanislaus Husch, Jr. and Ping-Fun Lam

Vol. 50 (1974), No. 1, 109–124

Let h be a self-homeomorphism of a compact n-dimensional manifold M, which is not homeomorphic to an odd dimensionaI sphere, such that the set N of irregular points of h is closed in M and the set of nonwandering points of h is zero-dimensional. One of the main results of this paper is that N is either connected or consists of the two fixed points of h. In the latter case, N is homeomorphic to the n-sphere. In the former case when n = 2, it is shown that each component of M N is an open 2-cell. If M is open and N is compact, then it is shown that M is homeomorphic to Euclidean n-space and N consists of a single fixed point of h.

Mathematical Subject Classification
Primary: 57A15
Secondary: 58F10
Received: 14 July 1972
Revised: 11 July 1973
Published: 1 January 1974
Lawrence Stanislaus Husch, Jr.
Ping-Fun Lam