Theorems · Theorem · general topology
denseRange_stoneCechUnit
∀ {α : Type u} [inst : TopologicalSpace α], DenseRange stoneCechUnitThe image of stoneCechUnit is dense. (But stoneCechUnit need
not be an embedding, for example if the original space is not Hausdorff.)
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 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.
Cites10
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
- DenseRangestatement · cited by 164
- Quot.mk_surjectiveproof · cited by 34
- Function.Surjective.denseRangeproof · cited by 21
- continuous_coinduced_rngproof · cited by 19
- StoneCechstatement · cited by 16
- stoneCechUnitstatement · cited by 15
- DenseRange.compproof · cited by 9
- T2Quotient.mkproof · cited by 8
- denseRange_preStoneCechUnitproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- isDenseInducing_stoneCechUnitproof · cited by 1
- StoneCech.projectiveproof · cited by 0
- stoneCech_hom_extproof · cited by 0