Theorems · Theorem · general topology
TopologicalSpace.Closeds.isAtom_coe
∀ {α : Type u_2} [inst : TopologicalSpace α] [T1Space α] {s : TopologicalSpace.Closeds α}, IsAtom ↑s ↔ IsAtom s- Defined in
- Mathlib.Topology.Sets.Closeds
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement · cited by 8,199
- T1Spacestatement and proof · cited by 275
- TopologicalSpace.Closedsstatement and proof · cited by 168
- IsAtomstatement and proof · cited by 130
- closure_singletonproof · cited by 8
- GaloisInsertion.isAtom_iff'proof · cited by 2
- Set.isAtom_iffproof · cited by 2
- TopologicalSpace.Closeds.giproof · cited by 1
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