Mathlib Map

Theorems · Theorem · general topology

Topology.IsOpenEmbedding.of_comp

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {g : Y → Z} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] (f : X → Y),
  Topology.IsOpenEmbedding g → Topology.IsOpenEmbedding (g ∘ f) → Topology.IsOpenEmbedding f
Defined in
Mathlib.Topology.Maps.Basic
Cited by
3 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceTopologicalSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.IsOpenImmersion.of_comp · cited by 2IsOpenImmersion.of_compCompHausLike.Sigma.isOpenEmbedding_ι · cited by 1Sigma.isOpenEmbedding_ιTopology.IsOpenEmbedding.nonemptyCompacts_map · cited by 0IsOpenEmbedding.nonemptyC…TopologicalSpace · cited by 24529TopologicalSpaceTopology.IsOpenEmbedding · cited by 231Topology.IsOpenEmbeddingTopology.IsOpenEmbedding.of_comp_iff · cited by 2IsOpenEmbedding.of_comp_i…IsOpenEmbedding.of_compCITED BYCITES

Cites3

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Cited by3

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