Theorems · Theorem · Lie groups
RestrictedProduct.continuous_inclusion
∀ {ι : Type u_1} {R : ι → Type u_2} {A : (i : ι) → Set (R i)} {𝓕 : Filter ι} [inst : (i : ι) → TopologicalSpace (R i)]
{𝓖 : Filter ι} (h : 𝓕 ≤ 𝓖), Continuous (RestrictedProduct.inclusion R A h)- Cited by
- 8 results in Mathlib
- Foundations
- Depth 69 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.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement and proof · cited by 8,121
- Continuousstatement · cited by 2,592
- iSupproof · cited by 2,415
- le_rflproof · cited by 1,558
- le_transproof · cited by 985
- Filter.principalproof · cited by 740
- iSup_congr_Propproof · cited by 247
- TopologicalSpace.inducedproof · cited by 148
- RestrictedProductstatement · cited by 117
Cited by8
Results whose statement or proof uses this declaration.
- RestrictedProduct.isEmbedding_inclusion_principalproof · cited by 1
- RestrictedProduct.isEmbedding_inclusion_topproof · cited by 1
- RestrictedProduct.continuous_dom_prod_leftproof · cited by 1
- RestrictedProduct.continuous_dom_prod_rightproof · cited by 1
- RestrictedProduct.weaklyLocallyCompactSpace_of_cofiniteproof · cited by 0
- RestrictedProduct.mapAlong_continuousproof · cited by 0
- RestrictedProduct.continuous_dom_piproof · cited by 0
- RestrictedProduct.continuous_dom_prodproof · cited by 0