Loogle!

Result

Found 19 declarations mentioning Topology.RelCWComplex.map.

• Topology.RelCWComplex.map 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : PartialEquiv (Fin n → ℝ) X
• Topology.RelCWComplex.map_zero_mem_closedCell 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : ↑(Topology.RelCWComplex.map n i) 0 ∈ Topology.RelCWComplex.closedCell n i
• Topology.RelCWComplex.map_zero_mem_openCell 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : ↑(Topology.RelCWComplex.map n i) 0 ∈ Topology.RelCWComplex.openCell n i
• Topology.RelCWComplex.closedCell_zero_eq_singleton 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [Topology.RelCWComplex C D] {j : Topology.RelCWComplex.cell C 0} : Topology.RelCWComplex.closedCell 0 j = {↑(Topology.RelCWComplex.map 0 j) ![]}
• Topology.RelCWComplex.openCell_zero_eq_singleton 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [Topology.RelCWComplex C D] {j : Topology.RelCWComplex.cell C 0} : Topology.RelCWComplex.openCell 0 j = {↑(Topology.RelCWComplex.map 0 j) ![]}
• Topology.RelCWComplex.continuousOn_symm 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : ContinuousOn (↑(Topology.RelCWComplex.map n i).symm) (Topology.RelCWComplex.map n i).target
• Topology.RelCWComplex.source_eq 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : (Topology.RelCWComplex.map n i).source = Metric.ball 0 1
• Topology.RelCWComplex.cellFrontier.eq_1 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : Topology.RelCWComplex.cellFrontier n i = ↑(Topology.RelCWComplex.map n i) '' Metric.sphere 0 1
• Topology.RelCWComplex.closedCell.eq_1 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : Topology.RelCWComplex.closedCell n i = ↑(Topology.RelCWComplex.map n i) '' Metric.closedBall 0 1
• Topology.RelCWComplex.openCell.eq_1 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C D : Set X} [Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : Topology.RelCWComplex.openCell n i = ↑(Topology.RelCWComplex.map n i) '' Metric.ball 0 1
• Topology.RelCWComplex.continuousOn 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : ContinuousOn (↑(Topology.RelCWComplex.map n i)) (Metric.closedBall 0 1)
• Topology.RelCWComplex.union' 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] : D ∪ ⋃ n, ⋃ j, ↑(Topology.RelCWComplex.map n j) '' Metric.closedBall 0 1 = C
• Topology.RelCWComplex.disjointBase' 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : Disjoint (↑(Topology.RelCWComplex.map n i) '' Metric.ball 0 1) D
• Topology.RelCWComplex.closed' 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (A : Set X) (asubc : A ⊆ C) : (∀ (n : ℕ) (j : Topology.RelCWComplex.cell C n), IsClosed (A ∩ ↑(Topology.RelCWComplex.map n j) '' Metric.closedBall 0 1)) ∧ IsClosed (A ∩ D) → IsClosed A
• Topology.RelCWComplex.mapsTo 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : ∃ I, Set.MapsTo (↑(Topology.RelCWComplex.map n i)) (Metric.sphere 0 1) (D ∪ ⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(Topology.RelCWComplex.map m j) '' Metric.closedBall 0 1)
• Topology.RelCWComplex.mapsto 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : ∃ I, Set.MapsTo (↑(Topology.RelCWComplex.map n i)) (Metric.sphere 0 1) (D ∪ ⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(Topology.RelCWComplex.map m j) '' Metric.closedBall 0 1)
• Topology.RelCWComplex.pairwiseDisjoint' 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u} {inst✝ : TopologicalSpace X} {C : Set X} {D : outParam (Set X)} [self : Topology.RelCWComplex C D] : Set.univ.PairwiseDisjoint fun ni => ↑(Topology.RelCWComplex.map ni.fst ni.snd) '' Metric.ball 0 1
• Topology.CWComplex.mapsTo 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C : Set X} [Topology.CWComplex C] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : ∃ I, Set.MapsTo (↑(Topology.RelCWComplex.map n i)) (Metric.sphere 0 1) (⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(Topology.RelCWComplex.map m j) '' Metric.closedBall 0 1)
• Topology.CWComplex.mapsto 📋 Mathlib.Topology.CWComplex.Classical.Basic
  {X : Type u_1} [t : TopologicalSpace X] {C : Set X} [Topology.CWComplex C] (n : ℕ) (i : Topology.RelCWComplex.cell C n) : ∃ I, Set.MapsTo (↑(Topology.RelCWComplex.map n i)) (Metric.sphere 0 1) (⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, ↑(Topology.RelCWComplex.map m j) '' Metric.closedBall 0 1)

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