Theorems · Theorem · general topology
TopologicalSpace.isOpen_univ
∀ {X : Type u} [self : TopologicalSpace X], TopologicalSpace.IsOpen Set.univThe set representing the whole space is an open set.
Use isOpen_univ in the root namespace instead.
- Defined in
- Mathlib.Topology.Defs.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 3 from the axioms · 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement · cited by 3,945
- TopologicalSpace.IsOpenstatement · cited by 25
Cited by2
Results whose statement or proof uses this declaration.
- isOpen_univproof · cited by 112
- TopologicalSpace.coinducedproof · cited by 56