Theorems · Definition · algebraic topology
Cube.splitAt
{N : Type u_1} → [DecidableEq N] → (i : N) → (N → ↑unitInterval) ≃ₜ ↑unitInterval × ({ j // j ≠ i } → ↑unitInterval)The forward direction of the homeomorphism between the cube $I^N$ and $I × I^{N\setminus\{j\}}$.
- Defined in
- Mathlib.Topology.Homotopy.HomotopyGroup
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- Set.Elemstatement and proof · cited by 7,166
- Homeomorphstatement · cited by 725
- unitIntervalstatement and proof · cited by 607
- Homeomorph.funSplitAtproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- GenLoop.fromLoopproof · cited by 8
- GenLoop.homotopyFromproof · cited by 2
- GenLoop.homotopyFrom_applystatement · cited by 1
- GenLoop.continuous_fromLoopproof · cited by 0
- GenLoop.to_fromproof · cited by 0
- GenLoop.fromLoop_applystatement · cited by 0
- GenLoop.fromLoop_coestatement · cited by 0
- GenLoop.homotopicFromproof · cited by 0