Theorems · Theorem · general topology
isOpen_ne
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {x : X}, IsOpen {y | y ≠ x}- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- TopologicalSpaceT1Space
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
- Set.ofPredstatement · cited by 6,101
- IsOpenstatement · cited by 2,400
- T1Spacestatement and proof · cited by 275
- isOpen_compl_singletonproof · cited by 27
Cited by22
Results whose statement or proof uses this declaration.
- Complex.differentiableAt_Gammaproof · cited by 8
- Continuous.isOpen_supportproof · cited by 8
- eventually_ne_nhdsproof · cited by 7
- Complex.hasStrictDerivAt_const_cpowproof · cited by 6
- Complex.differentiableOn_compl_singleton_and_continuousAt_iffproof · cited by 4
- hasStrictDerivAt_invproof · cited by 4
- Ne.nhdsWithin_compl_singletonproof · cited by 4
- Complex.norm_eqOn_of_isPreconnected_of_isMaxOnproof · cited by 3
- continuousWithinAt_update_of_neproof · cited by 3
- Complex.hasStrictFDerivAt_cpowproof · cited by 3
- MDifferentiableOn.norm_eqOn_of_isPreconnected_of_isMaxOnproof · cited by 2
- Ne.nhdsWithin_sdiff_singletonproof · cited by 2