The space of adding machines generated by continuous self maps of manifolds |
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Authors: | Emma D'Aniello |
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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 |
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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 . 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 .
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Keywords: | 39B12 54H20 |
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