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Theorems · Theorem · general topology

Filter.nhds_atTop

∀ {α : Type u_2} [inst : Preorder α], nhds Filter.atTop = ⨅ x, Filter.principal (Set.Iic (Filter.principal (Set.Ici x)))
Defined in
Mathlib.Topology.Filter
Cited by
2 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Filter.tendsto_nhds_atTop_iff · cited by 2Filter.tendsto_nhds_atTop…Filter.nhds_atBot · cited by 0Filter.nhds_atBotFilter · cited by 8121FilterPreorder · cited by 7952Preordernhds · cited by 5554nhdsFilter.atTop · cited by 2405Filter.atTopiInf · cited by 1690iInfSet.Iic · cited by 1111Set.IicSet.Ici · cited by 1070Set.IciFilter.principal · cited by 740Filter.principalFilter.nhds_principal · cited by 2Filter.nhds_principalFilter.nhds_iInf · cited by 2Filter.nhds_iInfFilter.nhds_atTopCITED BYCITES

Cites10

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Cited by2

Results whose statement or proof uses this declaration.