Properties of increasing sequence of Kirch-type topologies on the set of positive integers (Q2161373)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Properties of increasing sequence of Kirch-type topologies on the set of positive integers |
scientific article |
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Properties of increasing sequence of Kirch-type topologies on the set of positive integers (English)
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4 August 2022
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In the present paper the author examines properties of increasing sequences of Kirch-type topologies $D_m$ which are defined on $\mathbb{Z}^+$ that are subtopologies of Golomb's topology $D$. It is examined which of the spaces $(\mathbb{N},D)$ are semiregular and some conditions are given which are equivalent to continuity of non-constant polynomials $P:(\mathbb{N},D)\to(\mathbb{N},D)$ where $m\in\mathbb{N}$.
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Golomb's topology
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Kirch's topology
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Kirch-type topology
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continuity
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Darboux property
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polynomials
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regular open set
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semiregular space
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arithmetic progressions
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