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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.15595 |
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| _version_ | 1866909149135110144 |
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| author | Chacón-Tirado, Mauricio Piceno, César |
| author_facet | Chacón-Tirado, Mauricio Piceno, César |
| contents | In the literature, various types of points and meager sets whose complements are connected have been studied, such as colocally connected points, non-weak cut points/sets, non-block points/sets, shore points/sets, etc. We extend that study, in the following way: considering a continuum $X$ and a natural number $n$, we investigate sets $A \in 2^X$ meeting the criterion that $X - A$ has at most $n$ components, and we introduce degrees of connectivity of the complement of $A$. When $n=1$ and $A$ is meager or singleton, these new definitions are equivalent to the known definitions of non-cut points/sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connectivity degrees of complements of closed sets in continua Chacón-Tirado, Mauricio Piceno, César General Topology In the literature, various types of points and meager sets whose complements are connected have been studied, such as colocally connected points, non-weak cut points/sets, non-block points/sets, shore points/sets, etc. We extend that study, in the following way: considering a continuum $X$ and a natural number $n$, we investigate sets $A \in 2^X$ meeting the criterion that $X - A$ has at most $n$ components, and we introduce degrees of connectivity of the complement of $A$. When $n=1$ and $A$ is meager or singleton, these new definitions are equivalent to the known definitions of non-cut points/sets. |
| title | Connectivity degrees of complements of closed sets in continua |
| topic | General Topology |
| url | https://arxiv.org/abs/2403.15595 |