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Representations of spaces as function spaces

Published online by Cambridge University Press:  18 May 2009

M. P. Stannett
M. P. Stannett
Affiliation:
Department of Computer Science, The University, Sheffield, S3 7RH
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Given a topological space X, we can consider the group G(X) of all autohomeomorphisms of X. Much is known about the relationship between X and G(X) for certain restricted classes of the space X; Whittaker [7] has shown that the existence of an isomorphism between any two sufficiently large subgroups of G(X) and G(Y) implies that X and Y are actually homeomorphic, whenever these are both compact, locally Euclidean manifolds, with or without boundary; Fine and Schweigert [1] give a detailed analysis of G(ℝ); recently, Neumann [4], Mekler [3] and Truss [6] have considered in depth the group G(ℚ).

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 2 , May 1988, pp. 189 - 193
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Fine, N. J. and Schweigert, G. E., On the group of homeomorphisms of an arc, Ann. of Math. (2) 62 (1955), 237–253.CrossRefGoogle Scholar
2.Higgins, P. J., An introduction to topological groups, London Mathematical Society Lecture Note Series 15 (Cambridge, 1979).Google Scholar
3.Mekler, A. H., Groups embeddable in the autohomeomorphisms of ℚ, J. London Math. Soc. (2) 33 (1986), 49–58.CrossRefGoogle Scholar
4.Neumann, P. M., Automorphisms of the rational world, J. London Math. Soc. (2) 32 (1985), 439–448.Google Scholar
5.Shimrat, M., Embedding in homogeneous spaces, Quart, J. Math. Oxford Ser. (2) 5 (1954), 304–311.CrossRefGoogle Scholar
6.Truss, J. K., Embeddings of infinite permutation groups, Proceedings of Groups 1985 at St Andrews (to appear).Google Scholar
7.Whittaker, J. V., On isomorphic groups and homeomorphic spaces, Ann. of Math. (2) 78 (1963), 74–91.Google Scholar
8.Willard, S., General Topology, (Addison-Wesley, 1970).Google Scholar