# A new topology on the space of Lorentzian metrics on a fixed manifold

@article{Noldus2002ANT, title={A new topology on the space of Lorentzian metrics on a fixed manifold}, author={Johan Noldus}, journal={Classical and Quantum Gravity}, year={2002}, volume={19}, pages={6075-6107} }

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 the other, the difference in causal structure relative to a volume scale. These functions will distinguish two geometric properties of the Alexandrov sets A(p, q), (p, q) relative to two spacetime points q and p and metrics g and . It will be shown that this family generates uniformities and…

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