Fletcher, Samuel C.
(2016):
Similarity, Topology, and Physical Significance in Relativity Theory.
In: British Journal for the Philosophy of Science, Vol. 67, No. 2: pp. 365389

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Abstract
Stephen Hawking, among others, has proposed that the topological stability of a property of spacetime is a necessary condition for it to be physically significant. What counts as stable, however, depends crucially on the choice of topology. Some physicists have thus suggested that one should find a canonical topology, a single 'right' topology for every inquiry. While certain such choices might be initially motivated, some littlediscussed examples of Robert Geroch and some propositions of my own show that the main candidatesand each possible choice, to some extentfaces the horns of a nogo result. I suggest that instead of trying to decide what the 'right' topology is for all problems, one should let the details of particular types of problems guide the choice of an appropriate topology.