Theorems · Theorem · Lie groups
isClosed_setOfPred_map_mul
∀ (M₁ : Type u_6) (M₂ : Type u_7) [inst : TopologicalSpace M₂] [T2Space M₂] [inst_2 : Mul M₁] [inst_3 : Mul M₂]
[ContinuousMul M₂], IsClosed {f | ∀ (x y : M₁), f (x * y) = f x * f y}- Defined in
- Mathlib.Topology.Algebra.Monoid
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.ofPredstatement · cited by 6,101
- IsClosedstatement and proof · cited by 1,639
- T2Spacestatement and proof · cited by 1,351
- Set.iInterproof · cited by 1,084
- ContinuousMulstatement and proof · cited by 343
- continuous_applyproof · cited by 120
- isClosed_eqproof · cited by 71
- Set.ofPred_forallproof · cited by 48
- isClosed_iInterproof · cited by 43
- Continuous.fun_mulproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- isClosed_setOf_map_mulproof · cited by 0