# If it looks and smells like the reals...

Fundamenta Mathematicae (2000)

- Volume: 163, Issue: 1, page 1-11
- ISSN: 0016-2736

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topTall, Franklin. "If it looks and smells like the reals...." Fundamenta Mathematicae 163.1 (2000): 1-11. <http://eudml.org/doc/212426>.

@article{Tall2000,

abstract = {Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define $X_M$ to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if $X_M$ is homeomorphic to ℝ, then $X = X_M$. The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.},

author = {Tall, Franklin},

journal = {Fundamenta Mathematicae},

keywords = {elementary submodel; real line; locally compact separable metric space; local compactness; elementary submodel of set theory; separable metric spaces},

language = {eng},

number = {1},

pages = {1-11},

title = {If it looks and smells like the reals...},

url = {http://eudml.org/doc/212426},

volume = {163},

year = {2000},

}

TY - JOUR

AU - Tall, Franklin

TI - If it looks and smells like the reals...

JO - Fundamenta Mathematicae

PY - 2000

VL - 163

IS - 1

SP - 1

EP - 11

AB - Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define $X_M$ to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if $X_M$ is homeomorphic to ℝ, then $X = X_M$. The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.

LA - eng

KW - elementary submodel; real line; locally compact separable metric space; local compactness; elementary submodel of set theory; separable metric spaces

UR - http://eudml.org/doc/212426

ER -

## References

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