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NOTE ON TOTALLY DISCONNECTED AND CONNECTED SPACES

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강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2008.12|한국수학논문집 (Korean Journal of Mathematics)|제16권 제4호|pp. 495-498

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참고문헌

키워드

ErdÄos spacetotally disconnectedhomogeneous.
주제분류수학

초록

Every totally disconnected space is hereditarily discon- nected. In this note, we provide an example of a hereditarily discon- nected which is not a totally disconnected space. We further provide an example that not homogeneous space is the product of a totally disconnected and a connected.

Abstract

Every totally disconnected space is hereditarily discon- nected. In this note, we provide an example of a hereditarily discon- nected which is not a totally disconnected space. We further provide an example that not homogeneous space is the product of a totally disconnected and a connected.

참고문헌 (5)

  1. K. Kawamura, "On homogeneous to-tally disconnected 1-dimensional spaces", Fund. math, 150, pp.97~112 (1996)
  2. L. G. Oversteegen, "the dimension of certain totally disconnected spaces", Proc. Amer. math. Soc, 통권 : 122, pp.885~891 (1994)
  3. R. Pol, "There is no universal totally disconnected space", Fund. Math, 70, pp.265~267 (1973)
  4. P. ErdÄos, "The dimension of the rational points in Hilbert space", Annals of Math, 41, pp.734~736 (1940)
  5. W. Lewis, "Continuous curves of pseudo-arcs", Houston J. Math, 11, pp.91~99 (1985)

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