This paper describes our contribution to the Shared Task ReproGen by Belz et al. (2021), which investigates the reproducibility of human evaluations in the context of Natural Language Generation.
We show that, for vector spaces in which distance measurement is performed using a gauge, the existence of best coapproximations in $1$-codimensional closed linear subspaces implies in dimensions $\geq 2$ that the gauge is a norm, and in dimensions $\geq 3$ that the gauge is even a Hilbert space norm.
Metric Geometry Functional Analysis
Thus, this perturbation chain may be used to assess feature robustness.