More on Whitney levels of some decomposable continua

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-09-10 DOI:10.1016/j.topol.2024.109068

Alejandro Illanes , Eiichi Matsuhashi , Yoshiyuki Oshima

引用次数: 0

Abstract

In this paper, we show that there exists a non-D-continuum such that each positive Whitney level of the hyperspace of subcontinua of the continuum is both $D^{⁎}$ and Wilder. We show that the property of being continuum-wise Wilder is not a Whitney property, while it is a Whitney reversible property. Furthermore, we introduce the new class of continua: closed set-wise Wilder continua. This class is larger than the class of continuum chainable continua and smaller than the class of continuum-wise Wilder continua. In addition to the above results, we show that the Cartesian product of two closed set-wise Wilder continua is close set-wise Wilder.

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关于某些可分解连续体的惠特尼水平的更多信息

在本文中，我们证明存在一个非 D 连续统，使得连续统子连续统超空间的每个正惠特尼级既是 D⁎ 又是 Wilder。我们证明，连续度 Wilder 的性质不是惠特尼性质，而它是惠特尼可逆性质。此外，我们还引入了一类新的连续体：封闭集智 Wilder 连续体。这一类连续体比可链连续体大，比连续体-明智怀尔德连续体小。除了上述结果，我们还证明了两个闭集智怀尔德连续体的笛卡儿积是闭集智怀尔德连续体。

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.