Loogle!

Result

Found 12 declarations mentioning TopologicalSpace.NonemptyCompacts.map.

• TopologicalSpace.NonemptyCompacts.map 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] (f : α → β) (hf : Continuous f) (K : TopologicalSpace.NonemptyCompacts α) : TopologicalSpace.NonemptyCompacts β
• TopologicalSpace.NonemptyCompacts.map_id 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} [TopologicalSpace α] (K : TopologicalSpace.NonemptyCompacts α) : TopologicalSpace.NonemptyCompacts.map id ⋯ K = K
• TopologicalSpace.NonemptyCompacts.map_injective 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] {f : α → β} (hf : Continuous f) (hf' : Function.Injective f) : Function.Injective (TopologicalSpace.NonemptyCompacts.map f hf)
• TopologicalSpace.NonemptyCompacts.map_injective_iff 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] {f : α → β} (hf : Continuous f) : Function.Injective (TopologicalSpace.NonemptyCompacts.map f hf) ↔ Function.Injective f
• TopologicalSpace.NonemptyCompacts.toCompacts_map 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] (f : α → β) (hf : Continuous f) (K : TopologicalSpace.NonemptyCompacts α) : (TopologicalSpace.NonemptyCompacts.map f hf K).toCompacts = TopologicalSpace.Compacts.map f hf K.toCompacts
• TopologicalSpace.NonemptyCompacts.map_singleton 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] {f : α → β} (hf : Continuous f) (x : α) : TopologicalSpace.NonemptyCompacts.map f hf {x} = {f x}
• TopologicalSpace.NonemptyCompacts.coe_map 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] {f : α → β} (hf : Continuous f) (s : TopologicalSpace.NonemptyCompacts α) : ↑(TopologicalSpace.NonemptyCompacts.map f hf s) = f '' ↑s
• TopologicalSpace.NonemptyCompacts.map.congr_simp 📋 Mathlib.Topology.Sets.Compacts
  {α : Type u_1} {β : Type u_2} [TopologicalSpace α] [TopologicalSpace β] (f f✝ : α → β) (e_f : f = f✝) (hf : Continuous f) (K K✝ : TopologicalSpace.NonemptyCompacts α) (e_K : K = K✝) : TopologicalSpace.NonemptyCompacts.map f hf K = TopologicalSpace.NonemptyCompacts.map f✝ ⋯ K✝
• TopologicalSpace.NonemptyCompacts.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) (K : TopologicalSpace.NonemptyCompacts α) : TopologicalSpace.NonemptyCompacts.map (f ∘ g) ⋯ K = TopologicalSpace.NonemptyCompacts.map f hf (TopologicalSpace.NonemptyCompacts.map g hg K)
• UniformContinuous.nonemptyCompacts_map 📋 Mathlib.Topology.UniformSpace.Closeds
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : UniformContinuous f) : UniformContinuous (TopologicalSpace.NonemptyCompacts.map f ⋯)
• IsUniformInducing.nonemptyCompacts_map 📋 Mathlib.Topology.UniformSpace.Closeds
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) : IsUniformInducing (TopologicalSpace.NonemptyCompacts.map f ⋯)
• IsUniformEmbedding.nonemptyCompacts_map 📋 Mathlib.Topology.UniformSpace.Closeds
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformEmbedding f) : IsUniformEmbedding (TopologicalSpace.NonemptyCompacts.map f ⋯)

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 6ff4759 serving mathlib revision edaf32c