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Mathlib.Topology.Order.T5

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.

@[deprecated Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE (since := "2024-12-22")]

Alias of Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsGE.

@[deprecated Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLE (since := "2024-12-22")]

Alias of Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsLE.

@[deprecated Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhds (since := "2024-12-22")]

Alias of Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhds.

@[instance 100]

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

@[instance 100]