PreprintCC BY 4.0arXiv
C{à}dl{à}guity and compactness in submetric spaces
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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BibTeX
@misc{jakubowski2026càdlàguity,
title = {{Càdlàguity and compactness in submetric spaces}},
author = {Adam Jakubowski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33841},
eprint = {2609.33841},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33841},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - C{à}dl{à}guity and compactness in submetric spaces
AU - Adam Jakubowski
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33841
UR - https://arxiv.org/abs/2609.33841
AB - 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.
ER -