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Spacetimes as Topological Spaces, and the Need to Take Methods of General Topology More Seriously

In: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Author

Listed:
  • Kyriakos Papadopoulos

    (Kuwait University, Department of Mathematics)

  • Fabio Scardigli

    (Politecnico di Milano, Dipartimento di Matematica
    Leiden University, Institute-Lorentz for Theoretical Physics)

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 consider 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.

Suggested Citation

  • Kyriakos Papadopoulos & Fabio Scardigli, 2019. "Spacetimes as Topological Spaces, and the Need to Take Methods of General Topology More Seriously," Springer Books, in: Hemen Dutta & Ljubiša D. R. Kočinac & Hari M. Srivastava (ed.), Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, chapter 0, pages 185-196, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15242-0_6
    DOI: 10.1007/978-3-030-15242-0_6
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