Theorems · Theorem · general topology
t1Space_iff_continuous_cofinite_of
∀ {X : Type u_1} [inst : TopologicalSpace X], T1Space X ↔ Continuous ⇑CofiniteTopology.of- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 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.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Equivstatement · cited by 8,337
- nhdsproof · cited by 5,554
- Compl.complproof · cited by 2,925
- Continuousstatement and proof · cited by 2,592
- IsOpenproof · cited by 2,400
- Disjointproof · cited by 2,201
- IsClosedproof · cited by 1,639
- T1Spacestatement and proof · cited by 275
- T0Spaceproof · cited by 179
Cited by1
Results whose statement or proof uses this declaration.
- CofiniteTopology.continuous_ofproof · cited by 1