Theorems · Theorem · general topology
Set.Finite.isCompact_closure
∀ {X : Type u_1} [inst : TopologicalSpace X] [R0Space X] {s : Set X}, s.Finite → IsCompact (closure s)In an R₀ space, the closure of a finite set is a compact set.
- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceR0Space
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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
- Set.Finitestatement and proof · cited by 1,814
- IsCompactstatement · cited by 1,282
- closurestatement · cited by 1,254
- Bornologyproof · cited by 188
- R0Spacestatement and proof · cited by 22
- Set.Finite.isBoundedproof · cited by 4
- Bornology.relativelyCompactproof · cited by 3
- Bornology.relativelyCompact.isBounded_iffproof · cited by 1
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