The space of all self-homeomorphisms of a two-cell which fix the cellβs boundary is an absolute retract
HTML articles powered by AMS MathViewer
- by W. K. Mason
- Trans. Amer. Math. Soc. 161 (1971), 185-205
- DOI: https://doi.org/10.1090/S0002-9947-1971-0286067-9
- PDF | Request permission
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, On the deformation of an n-cell, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 406-407.
- R. D. Anderson, On topological infinite deficiency, Michigan Math. J. 14 (1967), 365β383. MR 214041, DOI 10.1307/mmj/1028999787 β, Spaces of homeomorphisms of finite graphs (to appear).
- 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, Γber eine Klasse von lokal zusammenhangenden RΓ€umen, Fund. Math. 19 (1932), 220-240.
- 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, On spaces of homeomorphisms, embeddings and functions (to appear).
- 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 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