What question did this study set out to answer?

This research aims to explore the relationship between intrinsic timed-Hausdorff convergence and other convergence types in timed-metric spaces.

May 17, 2026Open Access

Intrinsic timed-Hausdorff convergence and its implications

Key Points

This research aims to explore the relationship between intrinsic timed-Hausdorff convergence and other convergence types in timed-metric spaces.
Introduced distances between classes of Lorentzian manifolds using Hausdorff and Gromov–Hausdorff distances.
Analyzed implications of intrinsic timed-Hausdorff convergence on Gromov-Hausdorff and big bang convergence.
Intrinsic timed-Hausdorff convergence implies timeless Gromov–Hausdorff convergence.
Demonstrated implications for big bang convergence and other convergence types.

Abstract

Abstract Sakovich–Sormani introduced several notions of distance between certain classes of Lorentzian manifolds. These distances use the Hausdorff and Gromov–Hausdorff distances and, therefore, extend naturally to a broader class of spaces. Here we show that, for timed-metric-spaces, intrinsic timed–Hausdorff convergence implies (timeless) Gromov–Hausdorff convergence as well as big bang convergence, among other related implications for future-developed convergence.

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Authors

Raquel Perales

University of Vienna

Journals

Boletín de la Sociedad Matemática Mexicana

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Intrinsic timed-Hausdorff convergence and its implications

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Abstract

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