CardinalityLindelof.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Conjecture about cardinality of Lindelöf spaces

The conjecture asks for a Lindelöf Tychonoff space where all singletons are G_δ sets and which has cardinality > 𝔠.

This is Problem 1 in https://www.math.md/files/basm/y2013-n2-3/y2013-n2-3-(pp37-46).pdf.pdf

Reference:

Selected Old Open Problems in General Topology by A. V. Arhangel’skii

Imports (1)

FormalConjecturesUtil

theorem CardinalityLindelof.HasGδSingletons.lindelof_card Is there a Lindelöf Tychonoff space with singletons as Gδ sets with cardinality greater than the continuum? sorry line 47 source
Source documentation
Is there a Lindelöf Tychonoff space with singletons as Gδ sets with cardinality greater than the continuum?
Note: the cited paper uses a blanket convention that all spaces are Tychonoff.

depends on sorry what this means
Statement uses: Exists, TopologicalSpace, And, T35Space, HasGδSingletons, LindelofSpace, LT.lt, Cardinal, Cardinal.continuum, Cardinal.mk
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat, Nat
7 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem HasGδSingletons.lindelof_card :
    ∃ (X : Type) (_ : TopologicalSpace X),
      T35Space X ∧ HasGδSingletons X ∧ LindelofSpace X ∧ 𝔠 < #X := by
…
```
Mentions: HasGδSingletons