feat(Paper): conjecture about cardinality of Lindelöf spaces #1810
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Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
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| /-- | ||
| A space where all singletons are Gδ sets. | ||
| -/ | ||
| class HasGδSingletons (X : Type*) [TopologicalSpace X] : Prop where | ||
| isGδ_singleton : ∀ ⦃x : X⦄, IsGδ {x} | ||
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| /-- Singletons are Gδ in First-Countable T₁ Spaces- -/ | ||
| @[category test, AMS 54] | ||
| instance HasGδSingletons.of_t1Space_firstCountableTopology (X : Type*) [TopologicalSpace X] | ||
| [FirstCountableTopology X] [T1Space X] : HasGδSingletons X where | ||
| isGδ_singleton := IsGδ.singleton |
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Yeah, there are a few theorems one could add about this acutually
https://topology.pi-base.org/properties/P000191
I might add some later
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But I kind of prefer to put everything into the ForMathlib once all of #1849 is formalised (shouldnt take too long), to keep things organised better.
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I feel like it's easier to move things as they come, also from a reviewing perspective
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Closes #1809.
Two notes:
¬ ∃ (X : Type*) (_ : TopologicalSpace X) (_ : HasPointsGδ X) (_ : LindelofSpace X), 𝔠 < #Xwithout additional axioms.