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In mathematics, a sober space is a topological space X such that every (nonempty) irreducible closed subset of X is the closure of exactly one point of X: that is, every nonempty irreducible closed subset has a unique generic point.
Properties and examples, Definitions & Overview
Explore the main themes, entities and connections around Sober space. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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sober space every point irreducible unique closed topology topological prime net spaces set subsets open subset one completely closure t0
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Sober space | is a | topological space X such that every | 0.90 | text |
| Sober space | related to Definitions | Sober | 0.60 | section |
| Sober space | related to Definitions | In | 0.60 | section |
| Sober space | related to Definitions | T0 | 0.60 | section |
| Sober space | related to Definitions | Replacing | 0.60 | section |
| Sober space | related to Properties and examples | Any Hausdorff | 0.60 | section |
| Sober space | related to Properties and examples | T2 | 0.60 | section |
| Sober space | related to Properties and examples | Kolmogorov | 0.60 | section |
| Sober space | related to Properties and examples | T0 | 0.60 | section |
| Sober space | related to Properties and examples | Sobriety | 0.60 | section |
| Sober space | related to Properties and examples | T1 | 0.60 | section |
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