Loogle!

Result

Found 6 declarations mentioning TopologicalSpace.PositiveCompacts.map.

• TopologicalSpace.PositiveCompacts.map_id 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} [TopologicalSpace α] (K : TopologicalSpace.PositiveCompacts α) : TopologicalSpace.PositiveCompacts.map id ⋯ ⋯ K = K
• TopologicalSpace.PositiveCompacts.map 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] (f : α → β) (hf : Continuous f) (hf' : IsOpenMap f) (K : TopologicalSpace.PositiveCompacts α) : TopologicalSpace.PositiveCompacts β
• TopologicalSpace.PositiveCompacts.coe_map 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] {f : α → β} (hf : Continuous f) (hf' : IsOpenMap f) (s : TopologicalSpace.PositiveCompacts α) : ↑(TopologicalSpace.PositiveCompacts.map f hf hf' s) = f '' ↑s
• TopologicalSpace.PositiveCompacts.map_comp 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ] (f : β → γ) (g : α → β) (hf : Continuous f) (hg : Continuous g) (hf' : IsOpenMap f) (hg' : IsOpenMap g) (K : TopologicalSpace.PositiveCompacts α) : TopologicalSpace.PositiveCompacts.map (f ∘ g) ⋯ ⋯ K = TopologicalSpace.PositiveCompacts.map f hf hf' (TopologicalSpace.PositiveCompacts.map g hg hg' K)
• Basis.parallelepiped_map 📋 Mathlib.MeasureTheory.Measure.Haar.OfBasis
  {ι : Type u_1} {E : Type u_3} {F : Type u_4} [Fintype ι] [NormedAddCommGroup E] [NormedAddCommGroup F] [NormedSpace ℝ E] [NormedSpace ℝ F] (b : Basis ι ℝ E) (e : E ≃ₗ[ℝ] F) : (b.map e).parallelepiped = TopologicalSpace.PositiveCompacts.map ⇑e ⋯ ⋯ b.parallelepiped
• Basis.parallelepiped_eq_map 📋 Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
  {ι : Type u_1} {E : Type u_2} [Fintype ι] [NormedAddCommGroup E] [NormedSpace ℝ E] (b : Basis ι ℝ E) : b.parallelepiped = TopologicalSpace.PositiveCompacts.map ⇑b.equivFun.symm ⋯ ⋯ (TopologicalSpace.PositiveCompacts.piIcc01 ι)

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO.

This is Loogle revision 19971e9 serving mathlib revision bce1d65