The Katowice problem and autohomeomorphisms of

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• 作者：David Chodounský ; ^a ; ¹ ; ^{david.chodounsky@matfyz.cz" class="auth_mail" title="E-mail the corresponding author} ; Alan Dow^b ; ² ; ^{adow@uncc.edu" class="auth_mail" title="E-mail the corresponding author} ; ; Klaas Pieter Hart^c ; ^{k.p.hart@tudelft.nl" class="auth_mail" title="E-mail the corresponding author} ; ; Harm de Vries^d ; ^{vries101@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 54D40 ; secondary ; 03E05 ; 03E35 ; 06E05 ; 06E15 ; 54A35 ; 54D80
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 November 2016
• 年：2016
• 卷：213
• 期：Complete
• 页码：230-237
• 全文大小：316 K

文摘

We show that the existence of a homeomorphism between 4d0f57e712482f8a88f2e07">${\omega }_0^{⁎}$ and ${\omega }_1^{⁎}$ entails the existence of a non-trivial autohomeomorphism of 4d0f57e712482f8a88f2e07">${\omega }_0^{⁎}$. This answers Problem 441 in [8].

We also discuss the joint consistency of various consequences of 4d0f57e712482f8a88f2e07">${\omega }_0^{⁎}$ and ${\omega }_1^{⁎}$ being homeomorphic.