Theorems · Inductive type · general topology
NoncompactSpace
(X : Type u_1) → [TopologicalSpace X] → Prop
X is a noncompact topological space if it is not a compact space.
- Defined in
- Mathlib.Topology.Defs.Filter
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by23
Results whose statement or proof uses this declaration.
- IsCompact.ne_univstatement and proof · cited by 4
- noncompactSpace_of_neBotstatement · cited by 2
- MeasureTheory.measure_univ_of_isAddLeftInvariantstatement and proof · cited by 2
- noncompact_univstatement and proof · cited by 1
- not_compactSpace_iffstatement and proof · cited by 1
- exists_disjoint_smul_of_isCompactstatement and proof · cited by 1
- exists_disjoint_vadd_of_isCompactstatement and proof · cited by 1
- OnePoint.denseRange_coestatement and proof · cited by 1
- Topology.IsClosedEmbedding.noncompactSpacestatement and proof · cited by 1
- Metric.ediam_univ_eq_top_iff_noncompactstatement · cited by 1
- Metric.ediam_univ_of_noncompactstatement and proof · cited by 1
- MeasureTheory.measure_univ_of_isMulLeftInvariantstatement and proof · cited by 1