2018/04/30 by Kyriakos Papadopoulos, Fabio Scardigli · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.MP
paper · pdf · doi:10.1007/978-3-030-15242-0_6
Invited book Chapter, to appear in book: Current Trends in Mathematical Analysis and Its Interdisciplinary ApplicationsEdition: Birkhauser, imprint of Springer
arxiv created 2018/11/15 · arxiv updated 2019/09/17
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.