Theorems · Theorem · general topology
T5Space.of_forall_t4Space
∀ {X : Type u_1} [inst : TopologicalSpace X], (∀ (s : Set X), T4Space ↑s) → T5Space XAlias of the reverse direction of t5Space_iff_forall_t4Space.
A space is T5Space iff it is hereditarily T4Space.
- Defined in
- Mathlib.Topology.Separation.Regular
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites6
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
- Set.Elemstatement · cited by 7,166
- T4Spacestatement · cited by 12
- T5Spacestatement · cited by 7
- t5Space_iff_forall_t4Spaceproof · cited by 1
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