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Theorems · Theorem · general topology

specializes_comm

∀ {X : Type u_1} [inst : TopologicalSpace X] [R0Space X] {x y : X}, x ⤳ y ↔ y ⤳ x

In an R₀ space, the Specializes relation is symmetric, Iff version.

Defined in
Mathlib.Topology.Separation.Basic
Cited by
3 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceR0Space
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isCompact_closure_singleton · cited by 1isCompact_closure_singlet…addGroup_inseparable_iff · cited by 1addGroup_inseparable_iffgroup_inseparable_iff · cited by 0group_inseparable_iffTopologicalSpace · cited by 24529TopologicalSpaceSpecializes · cited by 176SpecializesR0Space · cited by 22R0SpaceSpecializes.symm · cited by 4Specializes.symmspecializes_commCITED BYCITES

Cites4

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Cited by3

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