Theorems · Theorem · general topology
EReal.continuous_coe_iff
∀ {α : Type u_1} [inst : TopologicalSpace α] {f : α → ℝ}, (Continuous fun a => ↑(f a)) ↔ Continuous f- Defined in
- Mathlib.Topology.Instances.EReal.Lemmas
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement · cited by 2,592
- ERealstatement · cited by 793
- Real.toERealstatement · cited by 303
- Topology.IsEmbedding.continuous_iffproof · cited by 21
- EReal.isEmbedding_coeproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Complex.isOpen_re_gt_ERealproof · cited by 4
- Complex.isOpen_im_lt_ERealproof · cited by 1
- Complex.isOpen_re_lt_ERealproof · cited by 1
- Complex.isOpen_im_gt_ERealproof · cited by 1