Theorems · Theorem · general topology
StableUnderGeneralization.preimage
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set Y},
StableUnderGeneralization s → Continuous f → StableUnderGeneralization (f ⁻¹' s)- Defined in
- Mathlib.Topology.Inseparable
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- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites7
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.preimagestatement · cited by 4,946
- Continuousstatement and proof · cited by 2,592
- StableUnderGeneralizationstatement and proof · cited by 24
- IsUpperSet.preimageproof · cited by 8
- Continuous.specialization_monotoneproof · cited by 3
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