Theorems · Theorem · general topology
Homeomorph.discreteTopology
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [DiscreteTopology X]
(h : X ≃ₜ Y), DiscreteTopology Y- Defined in
- Mathlib.Topology.Homeomorph.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Homeomorphstatement and proof · cited by 725
- DiscreteTopologystatement and proof · cited by 373
- Homeomorph.symmproof · cited by 365
- Homeomorph.isEmbeddingproof · cited by 73
- Topology.IsEmbedding.discreteTopologyproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Homeomorph.discreteTopology_iffproof · cited by 7
- Algebra.QuasiFinite.isDiscrete_comap_preimage_singletonproof · cited by 2
- IsEvenlyCovered.discreteTopology_fiberproof · cited by 1
- IsEvenlyCovered.of_fiber_homeomorphproof · cited by 1
- Real.finrank_eq_int_finrank_of_discreteproof · cited by 1