端点刚性的光滑风扇

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2023-10-02 DOI:10.4995/agt.2023.17922

Rodrigo Hernández-Gutiérrez, Logan C. Hoehn

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引用次数: 2

摘要

设X是一个光滑扇形，用E(X)表示它的端点集合。设E为下列空间之一:自然数，无理数，或康托集合与自然数的乘积。我们证明了有一个光滑扇形X使得E(X)同胚于E，并且对于每一个同胚h: X→X, h对E(X)的限制是恒等式。另一方面，我们也证明了如果X是任意光滑扇，使得E(X)同胚于完全Erdős空间，则X必然同胚于leelek扇;这是对Włodzimierz Charatonik 1989年的结果的补充。

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Smooth fans that are endpoint rigid

Let X be a smooth fan and denote its set of endpoints by E(X). Let E be one of the following spaces: the natural numbers, the irrational numbers, or the product of the Cantor set with the natural numbers. We prove that there is a smooth fan X such that E(X) is homeomorphic to E and for every homeomorphism h : X → X , the restriction of h to E(X) is the identity. On the other hand, we also prove that if X is any smooth fan such that E(X) is homeomorphic to complete Erdős space, then X is necessarily homeomorphic to the Lelek fan; this adds to a 1989 result by Włodzimierz Charatonik.

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来源期刊

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.