PreprintCC BY 4.0arXiv
A Metric Extension Theorem
Abstract
We show that, given a partially defined metric d:R→ℝ where R⊂ X2 is a closed equivalence relation on a compact metrizable space X, there is a metric d̂:X2→ ℝ such that d = d̂|R
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BibTeX
@misc{canel2026metric,
title = {{A Metric Extension Theorem}},
author = {Jacob Canel},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00344},
eprint = {2610.00344},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00344},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Metric Extension Theorem
AU - Jacob Canel
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00344
UR - https://arxiv.org/abs/2610.00344
AB - We show that, given a partially defined metric d:R→ℝ where R⊂ X^2 is a closed equivalence relation on a compact metrizable space X, there is a metric d̂:X^2→ ℝ such that d = d̂|_R
ER -