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Theorems · Theorem · general topology

MapClusterPt.exists_seq_tendsto

∀ {α : Type u} [t : TopologicalSpace α] [FirstCountableTopology α] {ι : Type u_1} {f : Filter ι}
  [f.IsCountablyGenerated] {x : α} {u : ι → α},
  MapClusterPt x f u → ∃ ψ, Filter.Tendsto (u ∘ ψ) Filter.atTop (nhds x) ∧ Filter.Tendsto ψ Filter.atTop f
Defined in
Mathlib.Topology.Bases
Cited by
2 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceFirstCountableTopologyFilter.IsCountablyGenerated
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Around this declaration

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

exists_seq_tendsto_liminf · cited by 1exists_seq_tendsto_liminfexists_seq_tendsto_limsup · cited by 0exists_seq_tendsto_limsupTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsFilter.Tendsto · cited by 3814Filter.TendstoFilter.atTop · cited by 2405Filter.atTopFilter.IsCountablyGenerated · cited by 220Filter.IsCountablyGenerat…FirstCountableTopology · cited by 106FirstCountableTopologyMapClusterPt · cited by 78MapClusterPtMapClusterPt.exists_seq_tends…CITED BYCITES

Cites8

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Cited by2

Results whose statement or proof uses this declaration.