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Theorems · Theorem · general topology

Inseparable.all

∀ {α : Type u} [inst : TopologicalSpace α] [IndiscreteTopology α] (x y : α), Inseparable x y

In the indiscrete topology no points are separable. The corresponding bot lemma is handled more generally by inseparable_iff_eq.

Defined in
Mathlib.Topology.Order
Cited by
2 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceIndiscreteTopology
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Around this declaration

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TopologicalSpace.indiscrete_iff_forall_inseparable · cited by 3TopologicalSpace.indiscre…inseparable_top · cited by 0inseparable_topTopologicalSpace · cited by 24529TopologicalSpaceInseparable · cited by 160InseparableIndiscreteTopology · cited by 43IndiscreteTopologyIndiscreteTopology.nhds_eq · cited by 2IndiscreteTopology.nhds_eqInseparable.allCITED BYCITES

Cites4

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Cited by2

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