- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Classical Metric Properties for Categories with the...
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Classical Metric Properties for Categories with the Interleaving Distance Cruz, Joshua
Description
Completeness, separability, and characterization of the precompact subsets are important for doing probability and statistics on a metric space, using tools like Prokhorov's Theorem. Recently in applied topology, a common type of (pseudo/quasi)metric space is an interleaving distance on a category. We relate the metric limit of a Cauchy sequence in such a space to the categorical limit of a corresponding diagram. Using this, we show that many familiar examples in the applied topology literature are metrically complete. We also study separability and precompactness for some familiar examples. Finally, we show how this new understanding can be used to prove results about probability and statistics on these spaces.
Item Metadata
Title |
Classical Metric Properties for Categories with the Interleaving Distance
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2018-08-10T15:35
|
Description |
Completeness, separability, and characterization of the precompact subsets are important for doing probability and statistics on a metric space, using tools like Prokhorov's Theorem. Recently in applied topology, a common type of (pseudo/quasi)metric space is an interleaving distance on a category. We relate the metric limit of a Cauchy sequence in such a space to the categorical limit of a corresponding diagram. Using this, we show that many familiar examples in the applied topology literature are metrically complete. We also study separability and precompactness for some familiar examples. Finally, we show how this new understanding can be used to prove results about probability and statistics on these spaces.
|
Extent |
26.0
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Duke University
|
Series | |
Date Available |
2019-03-24
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0377402
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Graduate
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International