The representation of homeomorphisms on the interval as finite compositions of involutions
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- by Sam W. Young PDF
- Proc. Amer. Math. Soc. 121 (1994), 605-610 Request permission
Abstract:
It is known that every homeomorphism on the interval is the composition of at most four involutions and that every decreasing homeomorphism is the composition of at most three involutions. We will characterize those homeomorphisms that are the composition of two involutions. It is then demonstrated that there exist three involutions that together generate a dense subgroup of the topological group of all homeomorphisms on the interval.References
- Sam W. Young, Finitely generated semigroups of continuous functions on $[0,\,1].$, Fund. Math. 68 (1970), 297–305. MR 267552, DOI 10.4064/fm-68-3-297-305
- N. J. Fine and G. E. Schweigert, On the group of homeomorphisms of an arc, Ann. of Math. (2) 62 (1955), 237–253. MR 72460, DOI 10.2307/1969678
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 605-610
- MSC: Primary 54H15; Secondary 54C05
- DOI: https://doi.org/10.1090/S0002-9939-1994-1243177-8
- MathSciNet review: 1243177