Characterizingω 1 and the long line by their topological elementary reflections
Tóm tắt
Given a topological space 〈X, T〉 ∈M, an elementary submodel of set theory, we defineX
Mto beX ∩M with the topology generated by {U ∩M : U ∈T ∩M}. We prove that it is undecidable whetherX
Mhomeomorphic toω
1 impliesX =X
M,yet it is true in ZFC that ifX
Mis homeomorphic to the long line, thenX =X
M.The former result generalizes to other cardinals of uncountable confinality while the latter generalizes to connected, locally compact, locally hereditarily LindelöfT
2 spaces.
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