Theorems · Theorem · general topology
MapClusterPt.of_comp
∀ {X : Type u} [inst : TopologicalSpace X] {α : Type u_1} {β : Type u_2} {F : Filter α} {u : α → X} {x : X} {φ : β → α}
{p : Filter β}, Filter.Tendsto φ p F → MapClusterPt x p (u ∘ φ) → MapClusterPt x F u- Defined in
- Mathlib.Topology.ClusterPt
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.mapproof · cited by 819
- MapClusterPtstatement and proof · cited by 78
- Filter.map_monoproof · cited by 63
- ClusterPt.monoproof · cited by 30
- MapClusterPt.clusterPtproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- tendsto_nhds_of_cauchySeq_of_subseqproof · cited by 6
- mapClusterPt_self_zpow_atTop_powproof · cited by 3
- mapClusterPt_self_zsmul_atTop_nsmulproof · cited by 3
- IsSeqCompact.isCountablyCompactproof · cited by 1