The diffeomorphism groups of the real line are pairwise bihomeomorphic
Abstract
We prove that the group D^r(R) of C^r diffeomorphisms of the real line, endowed with the compact-open and Whitney C^r topologies, is bihomeomorphic to the group H(R) of homeomorphisms of the real line endowed with the compact-open and Whitney topologies. This implies that the diffeomorphism group D^r(R) endowed with the Whitney C^r topology is homeomorphic to the countable box-power of the separable Hilbert space.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2008
- DOI:
- 10.48550/arXiv.0804.3645
- arXiv:
- arXiv:0804.3645
- Bibcode:
- 2008arXiv0804.3645B
- Keywords:
-
- Mathematics - Differential Geometry;
- Mathematics - General Topology;
- 57S05;
- 58D05;
- 58D15
- E-Print:
- 14 pages