Theorems · Theorem · general topology
compl_singleton_mem_codiscreteWithin
∀ {X : Type u_3} [inst : TopologicalSpace X] [T1Space X] {s : Set X} (x : X), {x}ᶜ ∈ Filter.codiscreteWithin sIn a T1Space, complements of singleton sets are codiscrete within any set.
- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
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Cites12
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
- Set.univproof · cited by 3,945
- Compl.complstatement · cited by 2,925
- Set.extproof · cited by 2,266
- T1Spacestatement and proof · cited by 275
- Filter.univ_memproof · cited by 96
- Filter.codiscreteWithinstatement · cited by 87
- sdiff_complproof · cited by 8
- codiscreteWithin_iff_locallyEmptyComplementWithinproof · cited by 3
- nhdsNE_of_nhdsNE_sdiff_finiteproof · cited by 3
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