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Theorems · Theorem · general topology

ClusterPt.neBot

∀ {X : Type u} [inst : TopologicalSpace X] {x : X} {F : Filter X}, ClusterPt x F → (nhds x ⊓ F).NeBot
Defined in
Mathlib.Topology.ClusterPt
Cited by
5 results in Mathlib
Foundations
Depth 49 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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

IsCompact.isClosed · cited by 77IsCompact.isClosedIsCompact.image_of_continuousOn · cited by 24IsCompact.image_of_contin…IsOpenMap.clusterPt_comap · cited by 3IsOpenMap.clusterPt_comapIsLindelof.image_of_continuousOn · cited by 1IsLindelof.image_of_conti…IsCountablyCompact.image · cited by 1IsCountablyCompact.imageTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsFilter.NeBot · cited by 853Filter.NeBotClusterPt · cited by 138ClusterPtClusterPt.neBotCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.