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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Open simple maps and periodic homeomorphisms


Author: John D. Baildon
Journal: Proc. Amer. Math. Soc. 39 (1973), 433-436
MSC: Primary 54C10; Secondary 57A05
DOI: https://doi.org/10.1090/S0002-9939-1973-0324626-2
MathSciNet review: 0324626
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Abstract: It is shown that an open map between $ 2$-manifolds without boundary that is the composition of $ n$ open simple (at most two-to-one) maps is necessarily of order 2". Since w=zz on the unit sphere is of order three, this shows an open map cannot necessarily be factored into a composition of open simple ones.


References [Enhancements On Off] (What's this?)

  • [1] K. A. Borsuk and R. Molski, On a class of continuous mappings, Fund. Math. 45 (1957), 84-98. MR 21 #858. MR 0102063 (21:858)
  • [2] J. W. Jaworowski, On simple regular mappings, Fund. Math. 45 (1958), 119-129. MR 21 #859. MR 0102064 (21:859)
  • [3] K. Sieklucki, On superpositions of simple mappings, Fund. Math. 48 (1960), 217-228. MR 22 #2981. MR 0112123 (22:2981)
  • [4] G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R.I., 1963. MR 32 #425. MR 0182943 (32:425)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0324626-2
Keywords: Simple map, finite-to-one map, periodic homeomorphism, superposition of maps, composition of maps, singular sets, fixed point sets, manifolds
Article copyright: © Copyright 1973 American Mathematical Society

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