Theorems · Theorem · general topology
IsGenericPoint.mem
∀ {α : Type u_1} [inst : TopologicalSpace α] {x : α} {S : Set α}, IsGenericPoint x S → x ∈ S- Defined in
- Mathlib.Topology.Sober
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- IsGenericPointstatement and proof · cited by 26
- specializes_rflproof · cited by 4
- IsGenericPoint.specializes_iff_memproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- IsGenericPoint.mem_open_set_iffproof · cited by 4
- Topology.IsOpenEmbedding.quasiSoberproof · cited by 2
- TopologicalSpace.IsOpenCover.quasiSober_iff_forallproof · cited by 1
- Topology.IsClosedEmbedding.quasiSoberproof · cited by 1
- IsGenericPoint.inseparableproof · cited by 1