Geometry of non-Hausdorff spaces and its significance for physics

  title={Geometry of non-Hausdorff spaces and its significance for physics},
  author={Michael Heller and Leszek Pysiak and Wiesław Sasin},
  journal={Journal of Mathematical Physics},
Hausdorff relation, topologically identifying points in a given space, belongs to elementary tools of modern mathematics. We show that if subtle enough mathematical methods are used to analyze this relation, the conclusions may be far-reaching and illuminating. Examples of situations in which the Hausdorff relation is of the total type, i.e., when it identifies all points of the considered space, are the space of Penrose tilings and space-times of some cosmological models with strong curvature… 

The Two-Faced God Janus or What Does n-Hausdorfness Have to Do With Dynamics and Topology?

The main work of the author in this part involves the many examples of spaces which satisfy a combinatorial separation axiom and also have (or lack) various other properties, such as being Lindelöf, first countable, compact, or being T1.

The Framework, Causal and Co-compact Structure of Space-time

We introduce a canonical, compact topology, which we call weakly causal, naturally generated by the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by certain

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The main idea of this work was to find dependencies, relationships and analogies between several branches of mathematics. First part of the work is concerned to the relationship between Formal

A New Causal Topology and Why the Universe is Co-compact

We show that there exists a canonical topology, naturally connected with the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by quantum gravity. Taking a

On the Proof of the Existence of Undominated Strategies in Normal Form Games

This paper correct, simplify, and generalize the second proof of Moulin by its reformulation in terms of topological convergence of nets by finding that the assertion now holds for almost compact spaces.

Gravity and Gauge

  • Nicholas J. Teh
  • Philosophy
    The British Journal for the Philosophy of Science
  • 2016
Philosophers of physics and physicists have long been intrigued by the analogies and disanalogies between gravitational theories and (Yang–Mills-type) gauge theories. Indeed, repeated attempts to

The Mattig Expression for a d-dimensional Gauss Bonnet FRWL Cosmology

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A sheaf of functions on a topological space is called a differential structure if it satisfies an axiom of a closure with respect to composition with the Euclidean functions. A differential structure

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We examine a class of two‐dimensional Lorentz manifolds which are ’’singular’’ in a certain sense. It is shown that, for such a manifold (M, g), the bundle boundary is a single point whose only

Quantum Gravity

General lectures on quantum gravity. 1 General Questions on Quantum Gravity It is not clear at all what is the problem in quantum gravity (cf. [3] or [8] for general reviews, written in the same

Groupoids, Inverse Semigroups, and their Operator Algebras

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The aim of this paper is to explain, mostly through examples, what groupoids are and how they describe symmetry. We will begin with elementary examples, with discrete symmetry, and end with examples

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Some points of the past Big Bang in the closed fourdimensional Friedman-model are found to be identical with points of the future collapse according to the bundle-boundary definition.


This is an introduction to some of the most probabilistic aspects of free probability theory.

The Role of Aesthetics in Pure and Applied Mathematical Research

  • Bull . Inst . Math . and Its Appl .
  • 1974

The Role of Aesthetics in Pure and Applied

  • Mathematical Research, Bull. Inst. Math. and Its Appl
  • 1974