On differential completions and compactifications of a differential space
Diana Dziewa-Dawidczyk, Zbigniew Pasternak-Winiarski
TL;DR
This paper introduces the concepts of differential completions and compactifications for differential spaces, proving the existence of maximal structures and providing conditions for completeness.
Contribution
It presents the first systematic study of differential completions and compactifications, establishing existence results and criteria for completeness in differential spaces.
Findings
Existence of maximal differential completion and compactification.
A sufficient condition for a differential space to admit a complete uniform differential structure.
Foundational results for the theory of differential completions and compactifications.
Abstract
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for the existence of a complete uniform differential structure on a given differential space is given.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems