Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CAUCHY COMPLETION OF CSASZAR FRAMES

  • CHUNG SE HWA (Department of Mathematics and Information Kyungwon University)
  • Published : 2005.02.01
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Abstract

We introduce a concept of Cauchy complete Csaszar frames and construct Cauchy completions of Csaszar frames using strict extensions of frames and show that the Cauchy completion gives rise to a coreflection in the categories CsFrm and UCsFrm.

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References

  1. J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley Interscience, New York, 1990
  2. B. Banschewski, Compactifications of frames, Math. Nachr. 149 (1990), 105-115 https://doi.org/10.1002/mana.19901490107
  3. B. Banschewski and S. S. Hong, Filters and strict extensions of frames, Kyungpook Math. J. 39 (1999) no. 1, 215-230
  4. B. Banschewski and A. Pultr, Cauchy points of uniform and nearness frames, Quaestions Math. 19 (1996), 101 127
  5. B. Banschewski and A. Pultr, Samuel compactification and completion of uniform frames, Math. Proc. Cambridge Phil. Soc. 108 (1990), 63-78 https://doi.org/10.1017/S030500410006895X
  6. S. H. Chung, Categories of syntopogenous spaces, Ph.D. Thesis, Sogang University, 1988
  7. A. Csaszar, Foundation of General Topology, MacMillan Company, New York, 1963
  8. S. S. Hong, Convergence in frames, Kyungpook Math. J. 35 (1995), 85-91
  9. S. S. Hong and Y. K. Kim, Cauchy completions of nearness frames, Applied Categorical Structures, 3 (1995), 371-377 https://doi.org/10.1007/BF00872906
  10. J. R. Isbell, Atomless parts of space, Math. Scand. 31 (1972), 5-32 https://doi.org/10.7146/math.scand.a-11409
  11. P. T. Johnstone, Stone Spaces, Cambridge Stud. Adv. Math. J. 3 (1982)
  12. S. A. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge University Press, Cambridge, 1970
  13. J. Picado, Structured frames by Weil Entourages, Applied Categorical Structures 8 (2000), 351-366 https://doi.org/10.1023/A:1008713430424
  14. J. W. Tukey, Convergence and Uniformity in Topology, Ann. Math. Stud. 2, Princeton University Press, 1940