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Theorems · Theorem · general topology

WithBot.nhds_coe

∀ {ι : Type u_1} [inst : LinearOrder ι] [inst_1 : TopologicalSpace ι] [inst_2 : OrderTopology ι] {r : ι},
  nhds ↑r = Filter.map WithBot.some (nhds r)
Defined in
Mathlib.Topology.Order.WithTop
Cited by
1 results in Mathlib
Foundations
Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderTopologicalSpaceOrderTopology
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Around this declaration

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

WithBot.tendsto_unbotD · cited by 2WithBot.tendsto_unbotDTopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrderFilter · cited by 8121Filternhds · cited by 5554nhdsWithBot · cited by 1498WithBotOrderTopology · cited by 1355OrderTopologyFilter.map · cited by 819Filter.mapWithBot.some · cited by 541WithBot.someTopology.IsOpenEmbedding.map_nhds_eq · cited by 22IsOpenEmbedding.map_nhds_…WithBot.isOpenEmbedding_coe · cited by 1WithBot.isOpenEmbedding_c…WithBot.nhds_coeCITED BYCITES

Cites10

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Cited by1

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