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TOPOLOGICAL PROPERTIES IN BCC-ALGEBRAS

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In this paper, we show how to associate certain topologieswith special ideals of BC -algebras on these BC -algebras. We showthat it is natural forBC -algebras to be topological BC -algebras withrespect to theses topologies. Furthermore, we show how certain standardproperties may arise. In addition we demonstrate that it is natural forthese topologies to have many clopen sets and thus to be highly connectedvia the ideal theory of BC -algebras.

Abstract

In this paper, we show how to associate certain topologieswith special ideals of BC -algebras on these BC -algebras. We showthat it is natural forBC -algebras to be topological BC -algebras withrespect to theses topologies. Furthermore, we show how certain standardproperties may arise. In addition we demonstrate that it is natural forthese topologies to have many clopen sets and thus to be highly connectedvia the ideal theory of BC -algebras.

참고문헌 (12)

  1. W. A. Dudek, "The number of subalgebras of finite BCC-algebras", Bull. Inst. Math. Academia Sinica, 20, pp.129~136 (1992)
  2. W. A. Dudeck, "On ideals and congruences in BCC-algebras", Czecho Math. J, 48(123), pp.21~29 (1998)
  3. J. Hao, "Ideal Theory of BCC-algebras", Sci. Math. Japo, 3, pp.373~381 (1998)
  4. Y. Imai, "On axiom system of propositional calculi XIV", Proc. Japan Academy, 42, pp.19~22 (1966)
  5. K. Is´eki, "An introduction to the theory of BCK-algebras", Math. Japon, 23, pp.1~26 (1978)
  6. Y. B. Jun, "Uniform structures in positive implication algebras", Intern. Math. J, 2(2), pp.215~219 (2002)
  7. Y. B. Jun, "On uniformities of BCK-algebras", Commun. Korean Math. Soc, 10(1), pp.11~14 (1995)
  8. Y. Komori, "The class of BCC-algebras is not a variety", Math. Japon, 29, pp.391~394 (1984)
  9. J. Meng, "BCK-algebras" (1994), Kyungmoonsa
  10. B. T. Sims, "Fundamentals of Topology" (1976), Macmillan Publishing Co., Inc
  11. A. Wro´nski, "BCK-algebras do not form a variety", Math. Japon, 28, pp.211~213 (1983)
  12. Dall Sun Yoon, "Uniform structures in $BCI$-algebras", 대한수학회논문집, 17(3), pp.403~407 (2002), 대한수학회

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