Cantor sets as generalized inverse limits
Tom 266 / 2024
Fundamenta Mathematicae 266 (2024), 1-24
MSC: Primary 54F17; Secondary 37B45, 37B10, 54F65, 54F15
DOI: 10.4064/fm230609-22-3
Opublikowany online: 14 June 2024
Streszczenie
We characterize when the inverse limit of a single set-valued function yields a Cantor set as its inverse limit. We do this by focusing on a subset of the domain we call {\rm D}(F). When {\rm D}(F) is finite, we are able to apply known results for shifts of finite type to obtain our results. We then adapt those concepts to an infinite, compact alphabet. We give general characterizations when {\rm D}(F) is countable and when {\rm D}(F) is uncountable. We include many examples illustrating these results.
