Hyperspaces of dimension 1

preprint2022arXivOpen access

Abstract

In a previuos paper the author asked if there exists a one-dimensional space XX that is not almost zero-dimensional, such that the dimension of the hyperspace of compact subsets of XX is one-dimensional. In this short note we give examples of spaces XX that are not almost zero-dimensional such that XX is one-dimensional and their hyperspace of compacta of XX also is one-dimensional.

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