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arXiv · 1805.08927

Assignments to sheaves of pseudometric spaces

Michael Robinson
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Abstract

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.

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Michael Robinson. 2018-05-23. Assignments to sheaves of pseudometric spaces. https://doi.org/10.32408/compositionality-2-2

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