Open simple maps and periodic homeomorphisms
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- by John D. Baildon PDF
- Proc. Amer. Math. Soc. 39 (1973), 433-436 Request permission
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
- Karol Borsuk and R. Molski, On a class of continuous mappings, Fund. Math. 45 (1957), 84–98. MR 102063, DOI 10.4064/fm-45-1-84-98
- J. W. Jaworowski, On simple regular mappings, Fund. Math. 45 (1958), 119–129. MR 102064, DOI 10.4064/fm-45-1-119-129
- K. Sieklucki, On superpositions of simple mappings, Fund. Math. 48 (1959/60), 217–228. MR 112123, DOI 10.4064/fm-48-2-217-228
- Gordon Thomas Whyburn, Analytic topology, American Mathematical Society Colloquium Publications, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR 0182943
Additional Information
- © Copyright 1973 American Mathematical Society
- 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