Theorems · Theorem · functional analysis
tendsto_norm_comp_cofinite_atTop_of_isClosedEmbedding
∀ {E : Type u_2} [inst : SeminormedAddGroup E] {X : Type u_5} [inst_1 : TopologicalSpace X] [DiscreteTopology X]
[ProperSpace E] {e : X → E}, Topology.IsClosedEmbedding e → Filter.Tendsto (norm ∘ e) Filter.cofinite Filter.atTop- Defined in
- Mathlib.Analysis.Normed.Group.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Filterproof · cited by 8,121
- Norm.normstatement and proof · cited by 5,413
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.atTopstatement and proof · cited by 2,405
- Filter.Tendsto.compproof · cited by 560
- DiscreteTopologystatement and proof · cited by 373
- SeminormedAddGroupstatement and proof · cited by 331
- Filter.cofinitestatement · cited by 251
- Topology.IsClosedEmbeddingstatement and proof · cited by 195
- ProperSpacestatement and proof · cited by 190
Cited by3
Results whose statement or proof uses this declaration.
- EisensteinSeries.linear_isTheta_leftproof · cited by 1
- EisensteinSeries.linear_isTheta_right_addproof · cited by 1
- EisensteinSeries.isLittleO_const_left_of_properSpace_of_discreteTopologyproof · cited by 1