Wilder continua and their subfamilies as coanalytic absorbers
Konrad Kr\'olicki, Pawe{\l} Krupski
TL;DR
This paper identifies Wilder continua and its subfamilies as coanalytic absorbers within the hyperspace of subcontinua of cubes, revealing their topological structure and homeomorphism to countable closed subsets of the unit interval.
Contribution
It establishes that Wilder continua and related subfamilies are coanalytic absorbers, providing new insights into their topological properties and classifications.
Findings
Wilder continua are coanalytic absorbers in hyperspaces.
Subfamilies are homeomorphic to nonempty countable closed subsets of the interval.
The results unify understanding of these continua's topological complexity.
Abstract
The family of Wilder continua in cubes of dimension > 2 and its two subfamilies-of continuum-wise Wilder continua and of hereditarily arcwise connected continua-are recognized as coanalytic absorbers in the hyperspace of subcontinua of the cubes. In particular, each of them is homeomorphic to the set of all nonempty countable closed subsets of the unit interval.
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