Theorems · Theorem · general topology
TopologicalSpace.NoetherianSpace.finite
∀ {α : Type u_1} [inst : TopologicalSpace α] [TopologicalSpace.NoetherianSpace α] [T2Space α], Finite αSpaces that are both Noetherian and Hausdorff are finite.
- Defined in
- Mathlib.Topology.NoetherianSpace
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univproof · cited by 3,945
- Finitestatement · cited by 3,029
- T2Spacestatement and proof · cited by 1,351
- TopologicalSpace.NoetherianSpacestatement and proof · cited by 23
- TopologicalSpace.NoetherianSpace.isCompactproof · cited by 5
- IsCompact.finite_of_discreteproof · cited by 4
- Finite.of_finite_univproof · cited by 4
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