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M， N， H

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-08 DOI:10.1016/j.topol.2025.109539

Will Brian , Alan Dow , Klaas Pieter Hart

引用次数: 0

摘要

让M = N×[0,1]。自然投影π:M→N，将（N, x）发送到N，推导出一个投影映射π:M→N，其中M和N分别表示M和N的Čech-Stone余数。我们证明了CH暗示了N的每一个自同胚通过自然投影提升到M的一个自同胚。也就是说，对于每一个同胚h:N→N，都存在一个h: M→M使得π°h =h°π。这补充了第二作者最近的一个结果，他表明这种提升特性不是ZFC的结果。结合这个提升定理和第一作者最近的一个结果，我们还证明了CH暗示H的一个序反转自同胚，H的半线H=[0，∞]的Čech-Stone余数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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M⁎, N⁎, and H⁎

Let

M = N \times [0, 1]

. The natural projection

π : M \to N

, which sends

(n, x)

to n, induces a projection mapping

π^{⁎} : M^{⁎} \to N^{⁎}

, where

M^{⁎}

and

N^{⁎}

denote the Čech-Stone remainders of

M

and

N

, respectively.

We show that

CH

implies every autohomeomorphism of

N^{⁎}

lifts through the natural projection to an autohomeomorphism of

M^{⁎}

. That is, for every homeomorphism

h : N^{⁎} \to N^{⁎}

there is a homeomorphism

H : M^{⁎} \to M^{⁎}

such that

π^{⁎} \circ H = h \circ π^{⁎}

. This complements a recent result of the second author, who showed that this lifting property is not a consequence of

ZFC

Combining this lifting theorem with a recent result of the first author, we also prove that

CH

implies there is an order-reversing autohomeomorphism of

H^{⁎}

, the Čech-Stone remainder of the half line

H = [0, \infty)

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.