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

2025/02/04 by Eiichi Matsuhashi, Matsuhashi, Eiichi
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.2502.01935

openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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