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The space of adding machines generated by continuous self maps of manifolds
Authors:Emma D'Aniello
Institution:a Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Via Vivaldi 43, 81100 Caserta, Italy
b Department of Mathematics, St. Olaf College, Northfield, MN 55057, United States
c Department of Mathematics, Weber State University, Ogden, UT 84408, United States
Abstract:Let M be the Cantor space or an n-dimensional manifold with C(M,M) the set of continuous self-maps of M, and View the MathML source. We prove the following:
(1)
If α≠∞, then Sα(M) is a nowhere dense subset of M×C(M,M) that contains no isolated points.
(2)
If α?β, then View the MathML source.
Keywords:39B12  54H20
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