Theorems · Theorem · general topology
Function.Surjective.denseRange
∀ {X : Type u_1} [inst : TopologicalSpace X] {α : Type u_4} {f : α → X}, Function.Surjective f → DenseRange fA surjective map has dense range.
- Defined in
- Mathlib.Topology.Continuous
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- closureproof · cited by 1,254
- DenseRangestatement · cited by 164
- IsClosed.closure_eqproof · cited by 139
- Function.Surjective.range_eqproof · cited by 70
Cited by21
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.denseRange_coeproof · cited by 9
- IsOpenQuotientMap.dense_preimage_iffproof · cited by 3
- denseRange_stoneCechUnitproof · cited by 3
- UniqueMDiffOn.uniqueMDiffOn_target_interproof · cited by 3
- denseRange_preStoneCechUnitproof · cited by 2
- ContinuousLinearMap.bijective_iff_dense_range_and_antilipschitzproof · cited by 1
- HasFDerivWithinAt.uniqueDiffWithinAt_of_continuousLinearEquivproof · cited by 1
- denseRange_idproof · cited by 1
- NumberField.InfinitePlace.Completion.denseRange_coeproof · cited by 1
- denseRange_zpow_iff_surjectiveproof · cited by 1
- Homeomorph.isDenseEmbeddingproof · cited by 1
- denseRange_zsmul_iff_surjectiveproof · cited by 1