Michael Robinson - Assignments to sheaves of pseudometric spaces

compositionality:13508 - Compositionality, June 2, 2020, Volume 2 (2020) - https://doi.org/10.32408/compositionality-2-2
Assignments to sheaves of pseudometric spacesArticle

Authors: Michael Robinson 1

  • 1 Mathematics and Statistics, American University, Washington, DC, USA

An assignment to a sheaf is the choice of a local section from each open set in the sheaf's base space, without regard to how these local sections are related to one another. This article explains that the consistency radius -- which quantifies the agreement between overlapping local sections in the assignment -- is a continuous map. When thresholded, the consistency radius produces the consistency filtration, which is a filtration of open covers. This article shows that the consistency filtration is a functor that transforms the structure of the sheaf and assignment into a nested set of covers in a structure-preserving way. Furthermore, this article shows that consistency filtration is robust to perturbations, establishing its validity for arbitrarily thresholded, noisy data.

Volume: Volume 2 (2020)
Published on: June 2, 2020
Imported on: May 2, 2024
Keywords: Mathematics - Algebraic Topology,Mathematics - Category Theory,55N05, 18F20

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