Theorems · Definition · general topology
IsOpen
{X : Type u} → [TopologicalSpace X] → Set X → PropIsOpen s means that s is open in the ambient topological space on X
- Defined in
- Mathlib.Topology.Defs.Basic
- Cited by
- 2,400 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- TopologicalSpace.IsOpenproof · cited by 25
Cited by2,628
Results whose statement or proof uses this declaration.
- interiorproof · cited by 714
- IsOpen.mem_nhdsstatement and proof · cited by 470
- Continuous.compproof · cited by 371
- tendsto_const_nhdsproof · cited by 330
- IsOpenMapproof · cited by 253
- Continuous.tendstoproof · cited by 206
- IsPreconnectedproof · cited by 205
- IsClopenproof · cited by 189
- TopologicalSpace.inducedproof · cited by 148
- IsOpen.preimagestatement and proof · cited by 147
- continuous_iff_continuousAtproof · cited by 139
- TopologicalSpace.Opens.is_open'statement · cited by 139
Showing the 200 most cited of 2,628.