Theorems · Inductive type · general topology
SequentialSpace
(X : Type u_1) → [TopologicalSpace X] → Prop
A topological space is said to be a sequential space if any sequentially closed set in this space is closed. This condition is weaker than being a Fréchet-Urysohn space.
- Defined in
- Mathlib.Topology.Defs.Sequences
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by24
Results whose statement or proof uses this declaration.
- IsSeqClosed.isClosedstatement and proof · cited by 9
- SeqContinuous.continuousstatement and proof · cited by 2
- continuous_iff_seqContinuousstatement and proof · cited by 1
- SequentialSpace.coinducedstatement and proof · cited by 1
- SequentialSpace.iSupstatement and proof · cited by 1
- SequentialSpace.isClosed_of_seqstatement and proof · cited by 1
- isClosed_iUnion_closure_singleton_of_not_tendstostatement and proof · cited by 1
- Sequential.mk.injstatement and proof · cited by 1
- Sequential.mk.noConfusionstatement and proof · cited by 1
- Sequential.casesOnstatement and proof · cited by 0
- isSeqClosed_iff_isClosedstatement and proof · cited by 0
- Sequential.noConfusionproof · cited by 0