Theorems · Theorem · Lie groups
RestrictedProduct.topologicalSpace_eq_of_principal
∀ {ι : Type u_1} {R : ι → Type u_2} {A : (i : ι) → Set (R i)} [inst : (i : ι) → TopologicalSpace (R i)] {S : Set ι},
RestrictedProduct.topologicalSpace R A (Filter.principal S) = TopologicalSpace.induced DFunLike.coe inferInstance- Cited by
- 5 results in Mathlib
- Foundations
- Depth 72 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- le_rflproof · cited by 1,558
- Filter.principalstatement and proof · cited by 740
- TopologicalSpace.inducedstatement and proof · cited by 148
- RestrictedProductstatement and proof · cited by 117
- TopologicalSpace.coinducedproof · cited by 56
- le_iSup₂_of_leproof · cited by 52
- continuous_iff_le_inducedproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- RestrictedProduct.isEmbedding_coe_of_principalproof · cited by 5
- RestrictedProduct.topologicalSpace_eq_iSupproof · cited by 2
- RestrictedProduct.continuous_domproof · cited by 1
- RestrictedProduct.topologicalSpace_eq_of_botproof · cited by 0
- RestrictedProduct.topologicalSpace_eq_of_topproof · cited by 0