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

Papadopoulos, Kyriakos; Scardigli, Fabio

doi:10.1007/978-3-030-15242-0_6

Cited by 3 publications

(3 citation statements)

References 37 publications

(75 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They sought answers to "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 [41]" shaped questions. In short, we should consider new topologies for the space-time…”

Section: Discussionmentioning

confidence: 99%

Monad Metrizable Space

Göçür

2020

Mathematics

View full text Add to dashboard Cite

Do the topologies of each dimension have to be same and metrizable for metricization of any space? I show that this is not necessary with monad metrizable spaces. For example, a monad metrizable space may have got any indiscrete topologies, discrete topologies, different metric spaces, or any topological spaces in each different dimension. I compute the distance in real space between such topologies. First, the passing points between different topologies is defined and then a monad metric is defined. Then I provide definitions and some properties about monad metrizable spaces and PAS metric spaces. I show that any PAS metric space is also a monad metrizable space. Moreover, some properties and some examples about them are presented.

show abstract

Section: Discussionmentioning

confidence: 99%

Monad Metrizable Space

Göçür

2020

Mathematics

View full text Add to dashboard Cite

show abstract

“…Consider the chronological order ≪, on a relativistic spacetime manifold M. Then, ≪ in ∩ B h ǫ (x). Low (see [5]) has shown that the Limit Curve Theorem fails to hold for the Path topology, and so the formation of a basic contradiction present in the proofs of all singularity theorems, fails as well (for a more extensive discussion see [11], [9] and [16]).…”

Section: Curved Spacetimesmentioning

confidence: 99%

On the Causal and Topological Structure of the 2-Dimensional Minkowski Space

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…For a critical survey on this discussion, we refer to[14].1 Natural vs. Artificial Topologies on a Relativistic Spacetime…”

mentioning

confidence: 99%

Natural vs. Artificial Topologies on a Relativistic Spacetime

Papadopoulos¹

2020

Springer Optimization and Its Applications

Self Cite

View full text Add to dashboard Cite

Consider a set M equipped with a structure * . We call a natural topology T * , on (M, * ), the topology induced by * . For example, a natural topology for a metric space (X, d) is a topology T d induced by the metric d and for a linearly ordered set (X, <) a natural topology should be the topology T < that is induced by the order <. This fundamental property, for a topology to be called "natural", has been largely ignored while studying topological properties of spacetime manifolds (M, g) where g is the Lorentz "metric", and the manifold topology T M has been used as a natural topology, ignoring the spacetime "metric" g. In this survey we review critically candidate topologies for a relativistic spacetime manifold, we pose open questions and conjectures with the aim to establish a complete guide on the latest results in the field, and give the foundations for future discussions. We discuss the criticism against the manifold topology, a criticism that was initiated by people like Zeeman, Göbel, Hawking-King-McCarthy and others, and we examine what should be meant by the term "natural topology" for a spacetime. Since the common criticism against spacetime topologies, other than the manifold topology, claims that there has not been established yet a physical theory to justify such topologies, we give examples of seemingly physical phenomena, under the manifold topology, which are actually purely effects depending on the choice of the topology; the Limit Curve Theorem, which is linked to singularity theorems in general relativity, and the Theorem of Gao-Wald type of "time dilation" are such examples.

show abstract

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

Cited by 3 publications

References 37 publications

Monad Metrizable Space

Monad Metrizable Space

On the Causal and Topological Structure of the 2-Dimensional Minkowski Space

Natural vs. Artificial Topologies on a Relativistic Spacetime

Contact Info

Product

Resources

About