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- In mathematics, the excluded point topology is a topology where exclusion of a particular point defines openness. Formally, let X be any non-empty set and p ∈ X. The collection of subsets of X is then the excluded point topology on X. There are a variety of cases which are individually named:
* If X has two points, it is called the Sierpiński space. This case is somewhat special and is handled separately.
* If X is finite (with at least 3 points), the topology on X is called the finite excluded point topology
* If X is countably infinite, the topology on X is called the countable excluded point topology
* If X is uncountable, the topology on X is called the uncountable excluded point topology A generalization is the open extension topology; if has the discrete topology, then the open extension topology on is the excluded point topology. This topology is used to provide interesting examples and counterexamples. (en)
- Нехай X — непорожня множина і p X. Точковилученою топологією на X називається топологія . (uk)
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- Нехай X — непорожня множина і p X. Точковилученою топологією на X називається топологія . (uk)
- In mathematics, the excluded point topology is a topology where exclusion of a particular point defines openness. Formally, let X be any non-empty set and p ∈ X. The collection of subsets of X is then the excluded point topology on X. There are a variety of cases which are individually named: A generalization is the open extension topology; if has the discrete topology, then the open extension topology on is the excluded point topology. This topology is used to provide interesting examples and counterexamples. (en)
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- Excluded point topology (en)
- Точковилучена топологія (uk)
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