Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A NOTE ON FOUR TYPES OF REGULAR RELATIONS

  • Song, H.S. (Department of Mathematics Kwangwoon University)
  • Received : 2012.03.17
  • Accepted : 2012.06.05
  • Published : 2012.06.30
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Abstract

In this paper, we study the four different types of relations, $\mathcal{P}(X,T)$, $\mathcal{R}(X,T)$, $\mathcal{L}(X,T)$, and $\mathcal{S}(X,T)$ in a transformation (X,T), and obtain some of their properties. In particular, we give a relationship between $\mathcal{R}(X,T)$ and $\mathcal{S}(X,T)$.

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References

  1. J. Auslander, Regular minimal sets 1, Trans. Amer. Math. Soc. 123 (1966), 469- 479. https://doi.org/10.1090/S0002-9947-1966-0193629-4
  2. I.U. Bronstein, Extension of minimal transformation groups, Sijthoff and Nordhoff Inter. Publ., Netherlands, 1979.
  3. J.P. Clay, Proximity relations in transformation groups, Trans. Amer. Math. Soc. 108 (1963), 88-96. https://doi.org/10.1090/S0002-9947-1963-0154269-3
  4. R. Ellis, Lectures on topological dynamics, Benjamin, New York, 1969.
  5. R. Ellis, A semigroup associated with a transformation group, Trans. Amer. Math. Soc. 94 (1960), 272-281. https://doi.org/10.1090/S0002-9947-1960-0123636-3
  6. R. Ellis and W.H. Gottschalk, Homomorphisms of transformation groups, Trans. Amer. Math. Soc. 94 (1960), 258-271. https://doi.org/10.1090/S0002-9947-1960-0123635-1
  7. S. Glasner, Compressibility properties in topological dynamics, Amer. J. Math. 97 (1975), 148-171. https://doi.org/10.2307/2373665
  8. P.S. Shoenfeld, Regular homomorphisms of minimal sets, Doctoral Dissertation, Univ. of Maryland (1974).
  9. J.O. Yu, Regular relations in transformation group, J. Korean Math. Soc. 21 (1984), 41-48.
  10. J.O. Yu, The regionally regular relations, J. Chungcheong Math. Soc. 19 (2006), 365-373.

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