Singular decomposable continua

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-10-21 DOI:10.1016/j.topol.2024.109110

引用次数: 0

Abstract

In this paper, we first provide an argument for the method used in [7] and [10] to blow up a point inside a subarc of a one-dimensional continuum to an arbitrary continuum. Next, we give an example of s Wilder continuum containing no strongly Wilder continua, no continuum-wise Wilder continua, no semiaposyndetic continua and no

D^{⁎}

-continua. Also, we provide an example of a continuum such that each positive Whitney level of the hyperspace of the continuum is strongly Wilder, although the continuum itself does not contain any Wilder continua.

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奇异可分解连续

本文首先论证了[7]和[10]中使用的将一维连续体子弧内的点炸成任意连续体的方法。接下来，我们举例说明一个不包含强怀尔德连续面、不包含连续面怀尔德连续面、不包含半不对称连续面和不包含 D⁎ 连续面的怀尔德连续面。此外，我们还举例说明了这样一个连续体：虽然连续体本身不包含任何怀尔德连续体，但连续体超空间的每个正惠特尼层都是强怀尔德连续体。

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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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.