Turbulence Phenomena in Real Analysis

The purpose of this paper is first to show that if X is any locally compact but not compact perfect Polish space and X 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 fEXg equivalent to limx[arrow]infinity f(x)/g(x...

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Bibliographic Details
Published in:Archive for mathematical logic 2005-10, Vol.44 (7), p.801-815
Main Author: Sofronidis, Nikolaos Efstathiou
Format: Article
Language:English
Subjects:
Mathematics
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Summary:The purpose of this paper is first to show that if X is any locally compact but not compact perfect Polish space and X 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 fEXg equivalent to limx[arrow]infinity f(x)/g(x)=1, where f, g are in C(X,R+*), then EX is induced by a turbulent Polish group action. Second we show that given any (n,r) belongs to N [times] ((N \{0}) union {infinity}), if we identify the n-dimensional unit sphere Sn with the one-point compactification of Rn via the stereographic projection, while En,r is the equivalence relation which is defined on the Polish group Cr(Rn,R+*) by fEn,rg equivalent to limx[arrow]infinity f(x)/g(x)=1, where f, g are in Cr(Rn,R+*),then En,r is also induced by a turbulent Polish group action. [PUBLICATION ABSTRACT]
ISSN:0933-5846
1432-0665
DOI:10.1007/s00153-005-0300-4