Compact spaces homeomorphic to their respective squares

We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact metrizable spaces. As our main result we show that there is a family of size continuum of pairwise non-homeomorphic compact...

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Bibliographic Details
Published inEuropean journal of mathematics Vol. 10; no. 2
Main Authors Dudák, Jan, Vejnar, Benjamin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2024
Subjects
Algebraic Geometry
Mathematics
Mathematics and Statistics
Research Article
Continuum
54E45
54F99
Compact space
Homeomorphism
54F15
Peano continuum
Zero-dimensional space
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Summary:We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact metrizable spaces. As our main result we show that there is a family of size continuum of pairwise non-homeomorphic compact metrizable zero-dimensional spaces homeomorphic to their respective squares. This answers a question of Włodzimierz J. Charatonik. We also discuss the situation in the classes of continua, Peano continua and absolute retracts.
ISSN:2199-675X
2199-6768
DOI:10.1007/s40879-024-00749-x