Theorems · Theorem · general topology
IsClosed.mk_lt_two_pow_mk_dense
∀ {X : Type u} [inst : TopologicalSpace X] [NormalSpace X] {s d : Set X},
IsClosed s → ∀ [DiscreteTopology ↑s], Dense d → Cardinal.mk ↑s < 2 ^ Cardinal.mk ↑d- Defined in
- Mathlib.Topology.Separation.NotNormal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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.Elemstatement and proof · cited by 7,166
- Cardinalstatement · cited by 2,598
- IsClosedstatement and proof · cited by 1,639
- Cardinal.mkstatement and proof · cited by 942
- LT.lt.trans_leproof · cited by 678
- DiscreteTopologystatement and proof · cited by 373
- Densestatement and proof · cited by 359
- NormalSpacestatement and proof · cited by 84
- Cardinal.cantorproof · cited by 12
- IsClosed.two_pow_mk_le_two_pow_mk_denseproof · cited by 2
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