Theorems · Theorem · general topology
IsSeqCompact.image
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
SeqContinuous f → ∀ {K : Set X}, IsSeqCompact K → IsSeqCompact (f '' K)Sequential compactness of sets is preserved under sequentially continuous functions.
- Defined in
- Mathlib.Topology.Sequences
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.imagestatement and proof · cited by 5,609
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- Filter.atTopproof · cited by 2,405
- StrictMonoproof · cited by 706
- Set.mem_image_of_memproof · cited by 371
- Filter.Tendsto.congrproof · cited by 70
- IsSeqCompactstatement and proof · cited by 26
- SeqContinuousstatement and proof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- IsSeqCompact.rangeproof · cited by 1