## The space of all self-homeomorphisms of a two-cell which fix the cellβs boundary is an absolute retract

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- by W. K. Mason
- Trans. Amer. Math. Soc.
**161**(1971), 185-205 - DOI: https://doi.org/10.1090/S0002-9947-1971-0286067-9
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## Abstract:

The theorem mentioned in the title is proved. A corollary of the title theorem is: any homeomorphism between two compact subsets of the function space mentioned in the title can be extended to a homeomorphism of the function space onto itself.## References

- J. W. Alexander,
- R. D. Anderson,
*On topological infinite deficiency*, Michigan Math. J.**14**(1967), 365β383. MR**214041**, DOI 10.1307/mmj/1028999787
β, - R. D. Anderson and R. H. Bing,
*A complete elementary proof that Hilbert space is homeomorphic to the countable infinite product of lines*, Bull. Amer. Math. Soc.**74**(1968), 771β792. MR**230284**, DOI 10.1090/S0002-9904-1968-12044-0 - Morton Brown,
*Pushing graphs around*, Conference on the Topology of Manifolds (Michigan State Univ., E. Lansing, Mich., 1967) Prindle, Weber & Schmidt, Boston, Mass., 1968, pp.Β 19β22. MR**0234468**
K. Borsuk, - C. H. Dowker,
*Mapping theorems for non-compact spaces*, Amer. J. Math.**69**(1947), 200β242. MR**20771**, DOI 10.2307/2371848 - Mary-Elizabeth Hamstrom and Eldon Dyer,
*Regular mappings and the space of homeomorphisms on a 2-manifold*, Duke Math. J.**25**(1958), 521β531. MR**96202** - Robert D. Edwards and Robion C. Kirby,
*Deformations of spaces of imbeddings*, Ann. of Math. (2)**93**(1971), 63β88. MR**283802**, DOI 10.2307/1970753
R. Geoghegan, - Mary-Elizabeth Hamstrom,
*Regular mappings and the space of homeomorphisms on a $3$-manifold*, Mem. Amer. Math. Soc.**40**(1961), 42. MR**152999** - Mary-Elizabeth Hamstrom,
*Some global properties of the space of homeomorphisms on a disc with holes*, Duke Math. J.**29**(1962), 657β662. MR**143185** - Olof Hanner,
*Some theorems on absolute neighborhood retracts*, Ark. Mat.**1**(1951), 389β408. MR**43459**, DOI 10.1007/BF02591376 - John G. Hocking and Gail S. Young,
*Topology*, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR**0125557** - Witold Hurewicz and Henry Wallman,
*Dimension Theory*, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR**0006493** - W. K. Mason,
*The space $H(M)$ of homeomorphisms of a compact manifold onto itself is homeomorphic to $H(M)$ minus any $\sigma$-compact set*, Amer. J. Math.**92**(1970), 541β551. MR**281234**, DOI 10.2307/2373359 - Ernest Michael,
*Continuous selections. II*, Ann. of Math. (2)**64**(1956), 562β580. MR**80909**, DOI 10.2307/1969603 - M. H. A. Newman,
*Elements of the topology of plane sets of points*, Cambridge, at the University Press, 1951. 2nd ed. MR**0044820** - George F. Simmons,
*Introduction to topology and modern analysis*, McGraw-Hill Book Co., Inc., New York-San Francisco, Calif.-Toronto-London 1963. MR**0146625** - A. H. Stone,
*Paracompactness and product spaces*, Bull. Amer. Math. Soc.**54**(1948), 977β982. MR**26802**, DOI 10.1090/S0002-9904-1948-09118-2 - Gordon Thomas Whyburn,
*Analytic Topology*, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR**0007095**, DOI 10.1090/coll/028

*On the deformation of an n-cell*, Proc. Nat. Acad. Sci. U.S.A.

**9**(1923), 406-407.

*Spaces of homeomorphisms of finite graphs*(to appear).

*Γber eine Klasse von lokal zusammenhangenden RΓ€umen*, Fund. Math.

**19**(1932), 220-240.

*On spaces of homeomorphisms, embeddings and functions*(to appear).

*Problems on infinite-dimensional spaces and manifolds*, Louisiana State University, Baton Rouge, La., 1969 (mimeographed).

## Bibliographic Information

- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**161**(1971), 185-205 - MSC: Primary 54.28
- DOI: https://doi.org/10.1090/S0002-9947-1971-0286067-9
- MathSciNet review: 0286067