Turbulence Phenomena in Real Analysis |
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Authors: | Nikolaos Efstathiou Sofronidis |
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Institution: | (1) , 19 Stratigou Makryianni Street, Thessaloniki, 54635, Greece |
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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 En,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 En,r is also induced by a turbulent Polish group action.
Dedicated to my sister Alexandra and to her daughter Marianthi. |
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Keywords: | Primary 03E15 22F05 Secondary 26B99 26E99 46A99 57R99 |
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