Theorems · Theorem · functional analysis
ContinuousMap.realToRCLike_inj
∀ {X : Type u_1} (𝕜 : Type u_2) [inst : TopologicalSpace X] [inst_1 : RCLike 𝕜] {f g : C(X, ℝ)},
ContinuousMap.realToRCLike 𝕜 f = ContinuousMap.realToRCLike 𝕜 g ↔ f = g- Defined in
- Mathlib.Analysis.RCLike.ContinuousMap
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceRCLike
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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
- ContinuousMap.realToRCLikestatement · cited by 18
- ContinuousMap.realToRCLikeOrderEmbeddingproof · cited by 7
- OrderEmbedding.eq_iff_eqproof · cited by 4
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