Theorems · Theorem · general topology
isClosedEmbedding_update
∀ {ι : Type u_3} {β : ι → Type u_4} [inst : DecidableEq ι] [inst_1 : (i : ι) → TopologicalSpace (β i)]
(x : (i : ι) → β i) (i : ι) [∀ (i : ι), T1Space (β i)], Topology.IsClosedEmbedding (Function.update x i)- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsClosedproof · cited by 1,639
- Function.updatestatement and proof · cited by 502
- continuous_constproof · cited by 278
- T1Spacestatement and proof · cited by 275
- Topology.IsClosedEmbeddingstatement · cited by 195
- continuous_idproof · cited by 192
- Function.update_injectiveproof · cited by 8
- Continuous.updateproof · cited by 7
- Topology.IsClosedEmbedding.of_continuous_injective_isClosedMapproof · cited by 7
- isClosed_set_piproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_pow_le_pow_lintegral_fderiv_auxproof · cited by 1