Theorems · Theorem · general topology
IsDiscrete.mono
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsDiscrete s → t ⊆ s → IsDiscrete tLet s, t ⊆ X be two subsets of a topological space X. If t ⊆ s and s is discrete,
then t is discrete.
(Compare DiscreteTopology.of_subset which is the same thing stated in terms of subtypes.)
- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 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
- IsDiscretestatement and proof · cited by 86
- IsDiscrete.to_subtypeproof · cited by 8
- DiscreteTopology.of_subsetproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Metric.finite_isBounded_inter_isClosedproof · cited by 4
- NumberField.Units.isMaxRank_iff_closure_finiteIndexproof · cited by 1
- IsCompact.inter_riemannZetaZeros_finiteproof · cited by 0