Theorems · Theorem · general topology
isClosed_sdiff_of_codiscreteWithin
∀ {X : Type u_1} [inst : TopologicalSpace X] {s U : Set X},
s ∈ Filter.codiscreteWithin U → IsClosed U → IsClosed (U \ s)If U is closed and s is codiscrete within U, then U \ s is closed.
- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Filterstatement · cited by 8,121
- Compl.complproof · cited by 2,925
- Filter.univ_mem'proof · cited by 1,672
- IsClosedstatement and proof · cited by 1,639
- Filter.mp_memproof · cited by 1,537
- Filter.codiscreteWithinstatement and proof · cited by 87
- isOpen_compl_iffproof · cited by 63
- eventually_nhdsWithin_iffproof · cited by 34
- Filter.eventually_iff_exists_memproof · cited by 28
- Filter.disjoint_principal_rightproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Function.locallyFinsuppWithin.closedSupportproof · cited by 1