Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

REGULARLY QUASI-ORDERED SPACES AND NORMALLY QUASI-ORDERED SPACES

  • Received : 2010.08.10
  • Accepted : 2010.08.30
  • Published : 2010.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Generalizing normally quasi-ordered spaces, we introduce a concept of regularly quasi-ordered spaces and study their categorical properties. We obtain well behaved reflective subcategories of the category Rqos of regularly quasi-ordered spaces and continuous isotones, namely the full subcategory of Rqos determined by $T_0$-objects among others, and this result can be extended to that in the category Nqos of normally quasi-ordered spaces and continuous isotones.

Keywords

References

  1. J. Adamek, H. Herrlich, and G. E. Strecker, Abstract and Concrete Categories, John Wiley and Sons, Inc., New York, 1990.
  2. N. Bourbaki, General Topology, Addison Wesley Pub. Co. Reading, Massachusetts, 1966.
  3. D. C. J. Burgess, and M. Fitzpatrick, On separation axioms for certain types of ordered topological space, Math. Proc. Camb. Phil. Soc. 82 (59) (1977), 59-65. https://doi.org/10.1017/S0305004100053688
  4. T. H. Choe, Partially ordered topological spaces, An. Acad. brasil. Cienc. 51 (1) (1979), 53-63.
  5. B. A. Davey, and H. A. Priestley, Introduction to Lattices and Order , Cambridge Univ. Press, New York, 1990.
  6. S. D. McCartan, Separation axioms for topological ordered spaces, Proc. Camb. Phil. Soc. 64 (1968), 965-973. https://doi.org/10.1017/S0305004100043668
  7. L. Nachbin, Topology and Order, D. Van Nostrand Co., Princeton, 1965.
  8. A. Schauerte, On the MacNeille completion of the category of partially ordered topological spaces, Math. Nachr. 163 (1993), 281-288. https://doi.org/10.1002/mana.19931630123
  9. S. H. Shin, Categorical properties of semi-continuous quasi-ordered spaces, Communications of the Korean Mathematical Society, 9 (2002), 85-90.
  10. S. H. Shin, Reflective subcategories of topological quasi-lattices , Korean Annals of Mathematics, 25 (2008), no. 2, 75-81.
  11. L. E. Ward Jr., Partially ordered topological spaces, Proc. Amer. Math. Soc. 5 (1954), 144-166. https://doi.org/10.1090/S0002-9939-1954-0063016-5