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A new topology on the space of Lorentzian metrics on a fixed manifold
We give a covariant definition of closeness between (time-oriented) Lorentzian metrics on a manifold M, using a family of functions which measure the difference in volume form on one hand and, on theExpand
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A Lorentzian Gromov–Hausdorff notion of distance
This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov?Hausdorff distanceExpand
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The moduli space of isometry classes of globally hyperbolic spacetimes
This paper is part of a research programme on the structure of the moduli space of Lorentzian geometries, a Lorentzian analogue of Gromov–Hausdorff theory based on the use of the Lorentz distance asExpand
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Lorentzian Manifolds and Causal Sets as Partially Ordered Measure Spaces
We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and theExpand
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A Proof of the Falsity of the Axiom of Choice.
We observe two things in this paper : namely that the Banach Tarski paradox is false and that the correct part of the proof leads to a violation of the axiomof choice.
0 50 81 04 v 1 2 6 A ug 2 00 5 A fully consistent relativistic quantum mechanics and a change of perspective on quantum gravity .
This paper can be seen as an exercise in how to adapt quantum mechanics from a strict relativistic perspective while being respectful and critical towards the experimental achievements of theExpand
A Higher Language for Mathematics.
We extend the language of mathematics by generalizing the logical implication and negation. As such, our framework serves as an extension of intuitionistic logic.
0 30 80 74 v 3 1 8 N ov 2 00 3 A Lorentzian Gromov-Hausdorff notion of distance
This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distanceExpand
0 30 80 74 v 1 2 2 A ug 2 00 3 A Lorentzian Lipschitz , Gromov-Hausdorff notion of distance
This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distanceExpand