Theorems · Theorem · general topology
continuousAt_fst
∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {p : X × Y},
ContinuousAt Prod.fst p- Defined in
- Mathlib.Topology.Constructions.SumProd
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- ContinuousAtstatement · cited by 697
- Continuous.continuousAtproof · cited by 297
- continuous_fstproof · cited by 103
Cited by15
Results whose statement or proof uses this declaration.
- ContinuousAt.fstproof · cited by 8
- Real.hasStrictFDerivAt_rpow_of_posproof · cited by 4
- Real.contDiffAt_rpow_of_neproof · cited by 4
- intervalIntegral.integral_hasStrictDerivAt_of_tendsto_ae_rightproof · cited by 3
- map_fst_nhdsproof · cited by 3
- Real.hasStrictFDerivAt_rpow_of_negproof · cited by 2
- exists_nhds_split_invproof · cited by 1
- Filter.Tendsto.fst_nhdsproof · cited by 1
- ContinuousAt.fst'proof · cited by 1
- ContinuousAt.fst''proof · cited by 1
- map_fst_nhdsWithinproof · cited by 1
- Filter.Eventually.prod_inl_nhdsproof · cited by 1