A fixed-point theorem for face maps, or deletion-tolerant random finite sets
Abstract
Abstract We establish a fixed-point theorem for the face maps that consist in deleting the i th entry of an ordered set. Furthermore, we show that there exists random finite sets of integers that are almost invariant under such deletions. Consequences for various monoids of order-preserving transformations of bold upper N N $\mathbf{N}$ are discussed in an appendix.
Fields of Study & Subjects
Advanced Topology and Set Theory
Limits and Structures in Graph Theory
DNA and Biological Computing
Publication details
- Journal / source
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Volume
- 181
- Issue
- 1
- Pages
- 751–772
- Publication date
- 26 March 2026
- Language
- EN