Geodesic
Representations of spaces as function spaces
Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 189-193

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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). 
Stannett, M. P. Representations of spaces as function spaces. Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 189-193. doi: 10.1017/S0017089500007217
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