TL;DR
This paper proves that all compactly generated future Cauchy horizons have past complete generators without requiring differentiability, advancing understanding of their geometric structure.
Contribution
It establishes the completeness of generators for compactly generated Cauchy horizons without differentiability assumptions, filling a gap in the geometric theory.
Findings
All compactly generated future Cauchy horizons have past complete generators.
The result holds without any differentiability conditions.
Dual statement for past Cauchy horizons is also proved.
Abstract
It is proved that every compactly generated future Cauchy horizon has past complete generators, and dually. No condition on the differentiability of the horizon is imposed.
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