On continuous polynomials of the Macías space
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910926474575872 |
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| author | Macías, Jhixon |
| author_facet | Macías, Jhixon |
| contents | Let $\mathbb{N}$ be the set of natural numbers. The Macías space $M(\mathbb{N})$ is the topological space $(\mathbb{N},τ_M)$ where $τ_M$ is generated by the collection of sets $σ_n := \{ m \in \mathbb{N} : \gcd(n, m) = 1 \}$. In this paper, we characterize the continuity of polynomials over $ M(\mathbb{N})$ and prove that the only continuous polynomials are monomials |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On continuous polynomials of the Macías space Macías, Jhixon General Topology Let $\mathbb{N}$ be the set of natural numbers. The Macías space $M(\mathbb{N})$ is the topological space $(\mathbb{N},τ_M)$ where $τ_M$ is generated by the collection of sets $σ_n := \{ m \in \mathbb{N} : \gcd(n, m) = 1 \}$. In this paper, we characterize the continuity of polynomials over $ M(\mathbb{N})$ and prove that the only continuous polynomials are monomials |
| title | On continuous polynomials of the Macías space |
| topic | General Topology |
| url | https://arxiv.org/abs/2503.17611 |