A conjugated version of the countable dense homogeneity |
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Authors: | Tadeusz Dobrowolski |
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Institution: | Department of Mathematics, Pittsburg State University, Pittsburg, KS 66762, USA Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warszawa, Poland |
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Abstract: | We are interested in finding a homeomorphism h of a space X with h−1○Φ○h(A)=B for a given bijection Φ of X and every pair of countable dense subsets A and B of X. For a separable Banach space X, such a homeomorphism h always exists provided the fixed-point set of Φ has the empty interior. Moreover, h can be chosen to be real-analytic. As a consequence, there exists a real analytic flow that sends A onto B after time t=1. Actually, for X=Rn, any bounded real-analytic vector field can be approximated by a real-analytic vector field whose induced flow sends A onto B after time t=1. Topological and Cp smooth counterparts of these results are also obtained. |
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Keywords: | 57N17 57N20 46A55 52A07 |
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