Homeomorphisms between finite powers of topological spaces

Orsatti, Adalberto; Rodinò, Nicola

doi:10.1016/0166-8641(85)90044-6

Cited by 9 publications

(3 citation statements)

References 4 publications

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“…Remark 3.4. Yet another proof of Theorem 3.2 can be obtained from the following general result by Orsatti and Rodinò [OR86]. They have shown that for every r ∈ N and every infinite cardinal number λ, there is a class C of size 2 λ of pairwise non-homeomorphic compact connected Hausdorff topological Abelian groups of weight λ with the property that for all m, n ∈ N and X ∈ C, X m is homeomorphic to X n if and only if m = n (mod r).…”

Section: Infinite Dimensional Casementioning

confidence: 99%

Compact spaces homeomorphic to their respective squares

Dudák,

Vejnar

2024

Preprint

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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 W. J. Charatonik. We also discuss the situation in the classes of continua, Peano continua and absolute retracts. 2020 Mathematics Subject Classification: Primary 54E45, Secondary 54F15 and 54F99.

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Section: Infinite Dimensional Casementioning

confidence: 99%

Compact spaces homeomorphic to their respective squares

Dudák,

Vejnar

2024

Preprint

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“…A short proof of Theorem 3.2 can be obtained from the following general result by Orsatti and Rodinò [20]: For every r ∈ N and every infinite cardinal number λ, there is a class C of size 2 λ of pairwise non-homeomorphic compact connected Hausdorff topological Abelian groups of weight λ with the property that for all m, n ∈ N and X ∈ C, X m is homeomorphic to X n if and only if m = n (mod r ). Hence, as every Hausdorff compact space of weight ω is metrizable, it suffices to take λ = ω and r = 1.…”

Section: Remark 33mentioning

confidence: 99%

Compact spaces homeomorphic to their respective squares

Dudák,

Vejnar

2024

European Journal of Mathematics

View full text Add to dashboard Cite

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.

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“…Her topological results are summarized in [18]. Answering a question of Trnková, Orsatti and Rodino showed in [11] that there is even a connected topological space homeomorphic to its cube but not its square. Koubek, Nešetřil, and Rödl [9] showed that the cube property fails for the class of partial orders, as well as for other classes of relational structures.…”

Section: Introductionmentioning

confidence: 99%