A TOPOLOGY FOR ENGEL EXPANSIONS: EVALUATION AND DIGIT CODING MAPS
Abstract
Abstract We develop a topological framework for Engel expansions that treats both directions of the correspondence between points of $(0,1]$ and nondecreasing digit sequences. We endow the sequence space with the product topology to study the evaluation map, and we fix a nonterminating digit algorithm to study the digit coding map. We also record the correspondence between cylinder sets and fundamental intervals and give an application to Baire category results for functions of the digits.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
semigroups and automata theory
Computability
Logic
AI Algorithms
Publication details
- Journal / source
- Bulletin of the Australian Mathematical Society
- Publisher
- Cambridge University Press (CUP)
- Pages
- 1–9
- Publication date
- 1 June 2026
- Language
- EN