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arXiv · 2609.33841

C{à}dl{à}guity and compactness in submetric spaces

Adam Jakubowski
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Abstract

A submetric space is a topological space equipped with a continuous metric that generates a metric topology weaker than the original one (e.g., a separable Hilbert space with the weak topology). In this paper, we systematically investigate the compactness-related properties of submetric spaces, which make this class of topological spaces a particularly suitable tool for probabilistic applications. As an illustration, we discuss in detail the compactness of the closure of a càdlàg trajectory taking values in a submetric space.

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Adam Jakubowski. 2026-09-27. C{à}dl{à}guity and compactness in submetric spaces. https://arxiv.org/abs/2609.33841

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