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Theorems · Theorem · general topology

OnePoint.isOpen_image_coe

∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsOpen (OnePoint.some '' s) ↔ IsOpen s
Defined in
Mathlib.Topology.Compactification.OnePoint.Basic
Cited by
1 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

OnePoint.isOpenMap_coe · cited by 1OnePoint.isOpenMap_coeSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.image · cited by 5609Set.imageIsOpen · cited by 2400IsOpenOnePoint · cited by 126OnePointSet.preimage_image_eq · cited by 87Set.preimage_image_eqOnePoint.some · cited by 76OnePoint.someOnePoint.coe_injective · cited by 6OnePoint.coe_injectiveOnePoint.infty_notMem_image_coe · cited by 4OnePoint.infty_notMem_ima…OnePoint.isOpen_iff_of_notMem · cited by 2OnePoint.isOpen_iff_of_no…OnePoint.isOpen_image_coeCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.