A non-D-continuum with weakly infinite-dimensional closed set-aposyndetic Whitney levels
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929697073397760 |
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| author | Matsuhashi, Eiichi |
| author_facet | Matsuhashi, Eiichi |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A non-D-continuum with weakly infinite-dimensional closed set-aposyndetic Whitney levels Matsuhashi, Eiichi General Topology 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]. |
| title | A non-D-continuum with weakly infinite-dimensional closed set-aposyndetic Whitney levels |
| topic | General Topology |
| url | https://arxiv.org/abs/2502.01935 |