Theorems · Theorem · general topology
continuous_const
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {y : Y}, Continuous fun x => y- Defined in
- Mathlib.Topology.Continuous
- Cited by
- 278 results in Mathlib
- Foundations
- Depth 68 from the axioms, rests on 779 definitions · 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
- Continuousstatement · cited by 2,592
- continuous_iff_continuousAtproof · cited by 139
- continuousAt_constproof · cited by 59
Cited by280
Results whose statement or proof uses this declaration.
- continuousOn_constproof · cited by 96
- continuous_normproof · cited by 36
- Continuous.prodMk_rightproof · cited by 32
- continuous_algebraMapproof · cited by 29
- Metric.isClosed_closedBallproof · cited by 28
- HasSum.mul_leftproof · cited by 25
- continuous_zeroproof · cited by 22
- continuousWithinAt_constproof · cited by 18
- continuous_real_toNNRealproof · cited by 15
- UpperHalfPlane.isOpen_upperHalfPlaneSetproof · cited by 14
- Continuous.prodMk_leftproof · cited by 14
- HasSum.mul_rightproof · cited by 11
Showing the 200 most cited of 280.