FREE HOMEOMORPHISMS OF TWO DIMENSIONAL MANIFOLDS

Abstract

M. Brown [2] posed an open question on the class of free homeomorphisms as follows: if f is a free homeomorphism of two manifold and k is a positive integer then is $f^{k}$ free\ulcorner In this paper we show that the answer of the open question is true.

Keywords

• Free homeomorphism;
• translation are;
• translation line;
• locally free homeomorphism

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References

1. Houston J. Math. v.10 A new proof of Brouwer's lemma on translation arc M. Brown
2. Houston J. Math. v.11 Homeomorphisms of two dimensional manifolds M. Brown
3. Proc. Amer. Math. Soc. v.123 A generalized translation theorem for free homeomorphisms of surface G. Lucien
4. Continuum Theory S. Nadler, Jr.
5. Trans. Amer. Math. Soc. v.306 A Brouwer Translation Theorem For Free Homeomorphisms E. Slaminka https://doi.org/10.1090/S0002-9947-1988-0927691-X