[Merged by Bors] - feat: composition of ContinuousMaps is inducing
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| #align continuous_map.continuous_comp ContinuousMap.continuous_comp | ||
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| /-- If `g : C(β, γ)` is a topology inducing map, then the composition | ||
| `ContinuousMap.comp g : C(α, β) → C(α, γ)` is a topology inducing map too. -/ | ||
| theorem inducing_comp (hg : Inducing g) : Inducing (g.comp : C(α, β) → C(α, γ)) where |
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Maybe call it Inducing.comp or Inducing.comp_fun to enable dot notation? Same thing for the next lemma.
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We already have Inducing.comp. Also, I guess some other bounded homs can have a similar property, and Inducing.comp_continuousMap leads to a longer call hg.comp_continuousMap instead of g.inducing_comp hg.
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If `g : C(β, γ)` is inducing, then `fun f : C(α, β) ↦ g.comp f` is inducing.
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ContinuousMaps is inducingContinuousMaps is inducing
kbuzzard
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If `g : C(β, γ)` is inducing, then `fun f : C(α, β) ↦ g.comp f` is inducing.
semorrison
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If `g : C(β, γ)` is inducing, then `fun f : C(α, β) ↦ g.comp f` is inducing.
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If
g : C(β, γ)is inducing, thenfun f : C(α, β) ↦ g.comp fis inducing.