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arXiv · 2502.01935

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

Eiichi Matsuhashi
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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].

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Eiichi Matsuhashi. 2025-02-04. A non-D-continuum with weakly infinite-dimensional closed set-aposyndetic Whitney levels. https://arxiv.org/abs/2502.01935

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