Theorems · Theorem · general topology
continuous_of_discreteTopology
∀ {α : Type u_1} [inst : TopologicalSpace α] [DiscreteTopology α] {β : Type u_2} [inst_2 : TopologicalSpace β]
{f : α → β}, Continuous f- Defined in
- Mathlib.Topology.Order
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimageproof · cited by 4,946
- Continuousstatement · cited by 2,592
- IsOpenproof · cited by 2,400
- DiscreteTopologystatement and proof · cited by 373
- isOpen_discreteproof · cited by 36
- continuous_defproof · cited by 21
Cited by22
Results whose statement or proof uses this declaration.
- ContinuousMap.equivFnOfDiscreteproof · cited by 5
- MeasureTheory.StronglyAdapted.isStronglyProgressive_of_discreteproof · cited by 5
- ultrafilter_extend_extendsproof · cited by 4
- Matrix.IsHermitian.cfc_eqproof · cited by 3
- Real.continuous_ofDigitsproof · cited by 1
- tendsto_mul_cofinite_nhds_zeroproof · cited by 1
- Metric.PiNatEmbed.continuous_distDenseSeqproof · cited by 1
- CategoryTheory.PreGaloisCategory.autEmbedding_range_isClosedproof · cited by 1
- CategoryTheory.PreGaloisCategory.has_decomp_quotientsproof · cited by 1
- Real.finrank_eq_int_finrank_of_discreteproof · cited by 1
- mdifferentiable_of_subsingletonproof · cited by 1
- TopologicalSpace.exists_isInducing_l_inftyproof · cited by 1