Theorems · Theorem · general topology
isCompact_range
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [CompactSpace X] {f : X → Y},
Continuous f → IsCompact (Set.range f)- Defined in
- Mathlib.Topology.Compactness.Compact
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.rangestatement · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- IsCompactstatement and proof · cited by 1,282
- CompactSpacestatement and proof · cited by 593
- Set.image_univproof · cited by 322
- IsCompact.imageproof · cited by 105
- isCompact_univproof · cited by 53
Cited by24
Results whose statement or proof uses this declaration.
- GromovHausdorff.ghDist_le_hausdorffDistproof · cited by 3
- LightProfinite.epi_iff_surjectiveproof · cited by 3
- PrimeSpectrum.isCompact_basicOpenproof · cited by 3
- Profinite.epi_iff_surjectiveproof · cited by 2
- CompHaus.epi_iff_surjectiveproof · cited by 2
- AlgebraicGeometry.compactSpace_iff_existsproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.isCompact_preimage_singletonproof · cited by 2
- Submodule.isCompact_of_fgproof · cited by 2
- bernsteinApproximation_uniformproof · cited by 1
- GromovHausdorff.ghDist_le_of_approx_subsetsproof · cited by 1
- AlgebraicGeometry.compactSpace_of_universallyClosedproof · cited by 1
- IsLocallyConstant.range_finiteproof · cited by 1