충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제24권2호
  • /
  • Pages.303-311
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  • 2011
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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THE UNIFORM DISTANCE SYSTEM WITH THE SYMMETRIC DISTANCE FUNCTION

  • Kim, Seungwook (Department of Mathematics, Hankuk University of Foreign Studies)
  • 투고 : 2011.03.09
  • 심사 : 2011.05.16
  • 발행 : 2011.06.30
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초록

Every topology is generated by a quasi-uniform distance system. The quasi-uniform distance system is a uniform distance system. The topology is uniformizable if and only if it is generated by the uniform distance system with the symmetric distance function.

키워드

참고문헌

  1. W. Hunsaker and W. Lindgren, Construction of quasi-uniformities, Math. Ann. 88 (1970), 39-42.
  2. S. Kim, Distance Sytems, Communications of the Korean Mathematical Society, 7 (1992), no. 1, 89-97.
  3. R. Nielsen and L. Sloyer, Quasi-uniformizability, Math. Ann. 182 (1969), 273- 274. https://doi.org/10.1007/BF01350703
  4. B. V. Querenburg, Mengentheoretische Topologie, Springer Verlag, 2001.