Theorems · Theorem · general topology
continuousAt_id
∀ {X : Type u_1} [inst : TopologicalSpace X] {x : X}, ContinuousAt id x- Defined in
- Mathlib.Topology.Continuous
- Cited by
- 28 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Quot.sound
- Assumes
- TopologicalSpace
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_idproof · cited by 192
Cited by28
Results whose statement or proof uses this declaration.
- continuousAt_id'proof · cited by 44
- Real.hasDerivAt_rpow_constproof · cited by 11
- Real.continuousAt_rpow_constproof · cited by 8
- hasFDerivAt_norm_rpowproof · cited by 5
- continuousAt_const_cpowproof · cited by 4
- continuousAt_cpow_constproof · cited by 3
- hasMFDerivAt_idproof · cited by 3
- Complex.continuousAt_cpow_const_of_re_posproof · cited by 2
- Complex.not_continuousAt_Gamma_zeroproof · cited by 2
- ZetaAsymptotics.term_welldefproof · cited by 2
- WeakFEPair.Λ_residue_zeroproof · cited by 2
- integral_gaussian_complexproof · cited by 2