单词 | Cantor Set | ||||||||||||||
释义 | Cantor SetThe Cantor set ( ![]() This produces the Set of Real Numbers
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The Cantor set is nowhere Dense, so it has Lebesgue Measure 0. A general Cantor set is a Closed Set consisting entirely of Boundary Points. Such setsare Uncountable and may have 0 or Positive Lebesgue Measure. The Cantor set is the only totallydisconnected, perfect, Compact Metric Space up to a Homeomorphism (Willard 1970). See also Alexander's Horned Sphere, Antoine's Necklace, Cantor Function
Boas, R. P. Jr. A Primer of Real Functions. Washington, DC: Amer. Math. Soc., 1996. Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, pp. 15-20, 1991. Willard, S. §30.4 in General Topology. Reading, MA: Addison-Wesley, 1970. |
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