Theorems · Theorem · general topology
IsOpenMap.isDiscrete_range
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
[DiscreteTopology X], IsOpenMap f → IsDiscrete (Set.range f)- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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
- Set.rangestatement · cited by 4,705
- DiscreteTopologystatement and proof · cited by 373
- Set.image_univproof · cited by 322
- IsOpenMapstatement and proof · cited by 253
- isOpen_univproof · cited by 112
- IsDiscretestatement and proof · cited by 86
- IsDiscrete.univproof · cited by 2
- IsDiscrete.image_of_isOpenMap_of_isOpenproof · cited by 1
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