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arXiv · 1804.05419

Spacetimes as topological spaces, and the need to take methods of general topology more seriously

Kyriakos Papadopoulos·Fabio Scardigli
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Abstract

Why is the manifold topology in a spacetime taken for granted? Why do we prefer to use Riemann open balls as basic-open sets, while there also exists a Lorentz metric? Which topology is a best candidate for a spacetime; a topology sufficient for the description of spacetime singularities or a topology which incorporates the causal structure? Or both? Is it more preferable to have a topology with as many physical properties as possible, whose description might be complicated and counterintuitive, or a topology which can be described via a countable basis but misses some important information? These are just a few from the questions that we ask in this Chapter, which serves as a critical review of the terrain and contains a survey with remarks, corrections and open questions.

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Kyriakos Papadopoulos, Fabio Scardigli. 2018-04-15. Spacetimes as topological spaces, and the need to take methods of general topology more seriously. https://doi.org/10.1007/978-3-030-15242-0_6

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