A non-D-continuum with weakly infinite-dimensional closed set-aposyndetic Whitney levels

TL;DR

This paper introduces a new class of continua called weakly infinite-dimensional closed set-aposyndetic continua and demonstrates their existence in relation to Whitney levels of hyperspaces, extending previous results in continuum theory.

Contribution

It defines the class of weakly infinite-dimensional closed set-aposyndetic continua and shows their occurrence in Whitney levels of hyperspaces, strengthening prior theorems.

Findings

Existence of a non-D-continuum with weakly infinite-dimensional Whitney levels

Extension of previous results by van Douwen, Goodykoontz, and Illanes

New class of continua introduced and characterized

Abstract

In this paper, we introduce the new class of continua; weakly infinite-dimensional closed set-aposyndetic continua. With this notion, we show that there exists a non-D-continuum such that each positive Whitney level of the hyperspace of the continuum is a weakly infinite-dimensional closed set-aposyndetic continuum. This result strengthens those of van Douwen and Goodykoontz [2], Illanes [7], and the main result of Illanes et al. [9].