# Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum

Fundamenta Mathematicae (1998)

- Volume: 155, Issue: 3, page 201-214
- ISSN: 0016-2736

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topFabel, Paul. "Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum." Fundamenta Mathematicae 155.3 (1998): 201-214. <http://eudml.org/doc/212252>.

@article{Fabel1998,

abstract = {We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic to the separable Hilbert space $l_2$.},

author = {Fabel, Paul},

journal = {Fundamenta Mathematicae},

keywords = {space of homeomorphisms of ; absolute retract},

language = {eng},

number = {3},

pages = {201-214},

title = {Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum},

url = {http://eudml.org/doc/212252},

volume = {155},

year = {1998},

}

TY - JOUR

AU - Fabel, Paul

TI - Self-homeomorphisms of the 2-sphere which fix pointwise a nonseparating continuum

JO - Fundamenta Mathematicae

PY - 1998

VL - 155

IS - 3

SP - 201

EP - 214

AB - We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic to the separable Hilbert space $l_2$.

LA - eng

KW - space of homeomorphisms of ; absolute retract

UR - http://eudml.org/doc/212252

ER -

## References

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- [8] W. B. R. Lickorish, A finite set of generators for the homeotopy group of a 2-manifold, Proc. Cambridge Philos. Soc. 60 (1964), 769-778. Zbl0131.20801
- [9] R. Luke and W. K. Mason, The space of homeomorphisms on a compact two-manifold is an absolute neighborhood retract, Trans. Amer. Math. Soc. 164 (1972), 273-285. Zbl0235.57002
- [10] W. K. Mason, The space of all self-homeomorphisms of a 2-cell which fix the cell's boundary is an absolute retract, ibid. 161 (1971), 185-205. Zbl0234.57016
- [11] C. Pommerenke, Boundary Behavior of Conformal Maps, Springer, Berlin, 1991.
- [12] D. J. Sprows, Isotopy groups of bounded 2-manifolds, Kumamoto J. Sci. (Math.) 15 (1983), 73-77. Zbl0528.57007
- [13] J. van Mill, Infinite Dimensional Topology, North-Holland, Amsterdam, 1989.

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