Theorems · Theorem · general topology
IsSeqCompact.range
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y}
[SeqCompactSpace X], SeqContinuous f → IsSeqCompact (Set.range f)The range of sequentially continuous function on a sequentially compact space is sequentially compact.
- Defined in
- Mathlib.Topology.Sequences
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.image_univproof · cited by 322
- IsSeqCompactstatement and proof · cited by 26
- SeqCompactSpacestatement and proof · cited by 7
- SeqContinuousstatement and proof · cited by 7
- SeqCompactSpace.isSeqCompact_univproof · cited by 3
- IsSeqCompact.imageproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- WeakDual.isSeqCompact_of_isBounded_of_isClosedproof · cited by 2