Theorems · Inductive type · general topology
T3Space
(X : Type u) → [TopologicalSpace X] → Prop
A T₃ space is a T₀ space which is a regular space. Any T₃ space is a T₁ space, a T₂ space, and a T₂.₅ space.
- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 51 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by55
Results whose statement or proof uses this declaration.
- IsDenseInducing.continuous_extendstatement and proof · cited by 5
- Summable.tsum_prod'statement and proof · cited by 5
- Summable.tsum_sigma'statement and proof · cited by 4
- IsDenseInducing.continuousAt_extendstatement and proof · cited by 3
- EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsumproof · cited by 3
- summable_sum_mul_antidiagonal_of_summable_mulstatement and proof · cited by 3
- tendsto_atTop_of_mapClusterPtstatement and proof · cited by 3
- HasSum.mulstatement and proof · cited by 3
- Summable.tsum_mul_tsumstatement and proof · cited by 3
- Summable.tsum_mul_tsum_eq_tsum_sum_antidiagonalstatement and proof · cited by 3
- Topology.IsEmbedding.t3Spacestatement and proof · cited by 3
- continuousWithinAt_leftLim_Iicstatement and proof · cited by 2