Theorems · Theorem · general topology
Topology.IsInducing.image_mem_nhdsWithin
∀ {X : Type u_1} {Y : Type u_2} {f : X → Y} [inst : TopologicalSpace Y] [inst_1 : TopologicalSpace X],
Topology.IsInducing f → ∀ {x : X} {s : Set X}, s ∈ nhds x → f '' s ∈ nhdsWithin (f x) (Set.range f)- Defined in
- Mathlib.Topology.Maps.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- Set.imagestatement · cited by 5,609
- nhdsstatement and proof · cited by 5,554
- Set.rangestatement · cited by 4,705
- nhdsWithinstatement · cited by 1,912
- Topology.IsInducingstatement and proof · cited by 266
- Filter.image_mem_mapproof · cited by 39
- Topology.IsInducing.map_nhds_eqproof · cited by 3
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