# Linear order is a completely normal Hausdorff topological space #

In this file we prove that a linear order with order topology is a completely normal Hausdorff topological space.

@[simp]
theorem Set.ordConnectedComponent_mem_nhds {X : Type u_1} [] [] [] {a : X} {s : Set X} :
s.ordConnectedComponent a nhds a s nhds a
theorem Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Ici {X : Type u_1} [] [] [] {a : X} {s : Set X} {t : Set X} (hd : Disjoint s ()) (ha : a s) :
(s.ordSeparatingSet t).ordConnectedSection nhdsWithin a ()
theorem Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iic {X : Type u_1} [] [] [] {a : X} {s : Set X} {t : Set X} (hd : Disjoint s ()) (ha : a s) :
(s.ordSeparatingSet t).ordConnectedSection nhdsWithin a ()
theorem Set.compl_section_ordSeparatingSet_mem_nhds {X : Type u_1} [] [] [] {a : X} {s : Set X} {t : Set X} (hd : Disjoint s ()) (ha : a s) :
(s.ordSeparatingSet t).ordConnectedSection nhds a
theorem Set.ordT5Nhd_mem_nhdsSet {X : Type u_1} [] [] [] {s : Set X} {t : Set X} (hd : Disjoint s ()) :
s.ordT5Nhd t
@[instance 100]
instance OrderTopology.completelyNormalSpace {X : Type u_1} [] [] [] :

A linear order with order topology is a completely normal Hausdorff topological space.

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@[instance 100]
instance OrderTopology.t5Space {X : Type u_1} [] [] [] :
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