Theorems · Theorem · general topology
IsLocallyConstant.iff_isOpen_fiber_apply
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {f : X → Y},
IsLocallyConstant f ↔ ∀ (x : X), IsOpen (f ⁻¹' {f x})- Defined in
- Mathlib.Topology.LocallyConstant.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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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
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Set.preimagestatement and proof · cited by 4,946
- Filter.Eventuallyproof · cited by 3,134
- IsOpenstatement and proof · cited by 2,400
- List.TFAE.outproof · cited by 177
- IsLocallyConstantstatement and proof · cited by 51
- IsLocallyConstant.tfaeproof · cited by 5
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