Theorems · Theorem · general topology
WithTop.isOpenEmbedding_some
∀ {α : Type u} [t : TopologicalSpace α] [inst : LinearOrder α] [inst_1 : OrderTopology α],
Topology.IsOpenEmbedding WithTop.someIf α has a linear order topology, some : α → WithTop α is an open embedding with respect to
the order topologies.
- Defined in
- Mathlib.Topology.EMetricSpace.Weak
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Top.topproof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement · cited by 3,754
- OrderTopologystatement and proof · cited by 1,355
- WithTop.somestatement · cited by 1,128
- Topology.IsOpenEmbeddingstatement · cited by 231
- WithTop.range_coeproof · cited by 19
- StrictMono.isEmbedding_of_ordConnectedproof · cited by 9
- WithTop.coe_strictMonoproof · cited by 8
- isOpen_Iio'proof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.