If it looks and smells like the reals...
Tall, Franklin
Fundamenta Mathematicae, Tome 163 (2000), p. 1-11 / Harvested from The Polish Digital Mathematics Library
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Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define XM to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if XM is homeomorphic to ℝ, then X=XM. The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212426 
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     title = {If it looks and smells like the reals...},
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     volume = {163},
     year = {2000},
     pages = {1-11},
     zbl = {0943.54005},
     language = {en},
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Tall, Franklin. If it looks and smells like the reals.... Fundamenta Mathematicae, Tome 163 (2000) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv163i1p1bwm/

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