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In mathematics, a weak Hausdorff space or weakly Hausdorff space is a topological space where the image of every continuous map from a compact Hausdorff space into the space is closed. The notion was introduced by M. C. McCord to remedy an inconvenience of working with the category of Hausdorff spaces. It is often used in tandem with compactly generated…
Overview, K-Hausdorff spaces & Δ-Hausdorff spaces
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hausdorff space closed compact every displaystyle weak k-hausdorff spaces continuous topological image kc subspace map k-closed subseteq topology subset compactly
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Weak Hausdorff space | completely T2 | (completely Hausdorff) | 1.00 | infobox |
| Weak Hausdorff space | T0 | (Kolmogorov) | 1.00 | infobox |
| Weak Hausdorff space | T1 | (Fréchet) | 1.00 | infobox |
| Weak Hausdorff space | T2 | (Hausdorff) | 1.00 | infobox |
| Weak Hausdorff space | T2½ | (Urysohn) | 1.00 | infobox |
| Weak Hausdorff space | T3 | (regular Hausdorff) | 1.00 | infobox |
| Weak Hausdorff space | T3½ | (Tychonoff) | 1.00 | infobox |
| Weak Hausdorff space | T4 | (normal Hausdorff) | 1.00 | infobox |
| Weak Hausdorff space | T5 | (completely normal Hausdorff) | 1.00 | infobox |
| Weak Hausdorff space | T6 | (perfectly normal Hausdorff) | 1.00 | infobox |
| Weak Hausdorff space | related to Δ-Hausdorff spaces | Hausdorff | 0.60 | section |
| Weak Hausdorff space | related to Δ-Hausdorff spaces | Every | 0.60 | section |
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