Theorems · Definition · functional analysis
ContinuousMap.realToRCLikeOrderEmbedding
(X : Type u_1) → (𝕜 : Type u_2) → [inst : TopologicalSpace X] → [inst_1 : RCLike 𝕜] → C(X, ℝ) ↪o C(X, 𝕜)
ContinuousMap.realToRCLike as an order embedding.
- Defined in
- Mathlib.Analysis.RCLike.ContinuousMap
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceRCLike
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
- RCLikestatement and proof · cited by 2,829
- ContinuousMapstatement and proof · cited by 2,491
- OrderEmbeddingstatement · cited by 619
- RCLike.toPartialOrderstatement · cited by 106
- ContinuousMap.realToRCLikeproof · cited by 18
Cited by7
Results whose statement or proof uses this declaration.
- ContinuousMap.realToRCLikeOrderEmbedding_applystatement and proof · cited by 0
- ContinuousMap.realToRCLike_injproof · cited by 0
- ContinuousMap.realToRCLike_injectiveproof · cited by 0
- ContinuousMap.realToRCLike_le_realToRCLike_iffproof · cited by 0
- ContinuousMap.realToRCLike_lt_realToRCLike_iffproof · cited by 0
- ContinuousMap.realToRCLike_monotoneproof · cited by 0
- ContinuousMap.realToRCLike_strictMonoproof · cited by 0