Theorems · Theorem · general topology
OnePoint.isClosed_iff_of_notMem
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set (OnePoint X)},
OnePoint.infty ∉ s → (IsClosed s ↔ IsClosed (OnePoint.some ⁻¹' s) ∧ IsCompact (OnePoint.some ⁻¹' s))- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
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Cites13
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
- Set.preimagestatement and proof · cited by 4,946
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- compl_complproof · cited by 229
- OnePointstatement and proof · cited by 126
- OnePoint.inftystatement and proof · cited by 102
- OnePoint.somestatement and proof · cited by 76
- isOpen_compl_iffproof · cited by 63
- Set.preimage_complproof · cited by 43
- Set.mem_complproof · cited by 18
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