Assignments to sheaves of pseudometric spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866916347091353600 |
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| author | Robinson, Michael |
| author_facet | Robinson, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_08927 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Assignments to sheaves of pseudometric spaces Robinson, Michael Algebraic Topology Category Theory 55N05, 18F20 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. |
| title | Assignments to sheaves of pseudometric spaces |
| topic | Algebraic Topology Category Theory 55N05, 18F20 |
| url | https://arxiv.org/abs/1805.08927 |