Theorems · Theorem · general topology
TopologicalSpace.IrreducibleCloseds.mk_singleton
∀ {α : Type u_2} [inst : TopologicalSpace α] [inst_1 : T1Space α] {x : α},
{ carrier := {x}, isIrreducible' := ⋯, isClosed' := ⋯ } = {x}- Defined in
- Mathlib.Topology.Sets.Closeds
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- TopologicalSpaceT1Space
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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
- T1Spacestatement and proof · cited by 275
- isClosed_singletonstatement · cited by 66
- TopologicalSpace.IrreducibleClosedsstatement · cited by 30
- isIrreducible_singletonstatement · cited by 4
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