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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).

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

References

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