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Turbulence Phenomena in Real Analysis

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Abstract

The purpose of this paper is first to show that if X is any locally compact but not compact perfect Polish space and stands for the one-point compactification of X, while EX is the equivalence relation which is defined on the Polish group C(X,R+*) by where f, g are in C(X,R+*), then EX is induced by a turbulent Polish group action. Second we show that given any if we identify the n-dimensional unit sphere Sn with the one-point compactification of Rn via the stereographic projection, while E n , r is the equivalence relation which is defined on the Polish group Cr(Rn,R+*) by where f, g are in Cr(Rn,R+*), then E n , r is also induced by a turbulent Polish group action.

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  1.  , 19 Stratigou Makryianni Street, Thessaloniki, 54635, Greece

    Nikolaos Efstathiou Sofronidis

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  1. Nikolaos Efstathiou Sofronidis
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Correspondence to Nikolaos Efstathiou Sofronidis.

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Dedicated to my sister Alexandra and to her daughter Marianthi.

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Sofronidis, N. Turbulence Phenomena in Real Analysis. Arch. Math. Logic 44, 801–815 (2005). https://doi.org/10.1007/s00153-005-0300-4

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  • DOI: https://doi.org/10.1007/s00153-005-0300-4

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