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An elementary proof of a theorem of S. Mardešić

Author: Jacek Nikiel
Journal: Proc. Amer. Math. Soc. 101 (1987), 385-386
MSC: Primary 54B25; Secondary 54F05
MathSciNet review: 902546
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Abstract: A simple proof is given of the following theorem of S. Mardešić: Each arc is an inverse limit of some inverse system of copies of $ [0,1]$ with monotone bonding maps.

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  • [1] Ryszard Engelking, General topology, PWN—Polish Scientific Publishers, Warsaw, 1977. Translated from the Polish by the author; Monografie Matematyczne, Tom 60. [Mathematical Monographs, Vol. 60]. MR 0500780
  • [2] John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
  • [3] Sibe Mardešić, Locally connected ordered and chainable continua, Rad Jugoslav. Akad. Znan. Umjet. Odjel Mat. Fiz. Tehn. Nauke 319 (1961), 147–166 (Serbo-Croatian, with English summary). MR 0148036

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Keywords: Arc, inverse system, monotone map
Article copyright: © Copyright 1987 American Mathematical Society