An irrational problem

Franklin D. Tall. "An irrational problem." Fundamenta Mathematicae 175.3 (2002): 259-269. <http://eudml.org/doc/282913>.

@article{FranklinD2002,
abstract = {Given a topological space ⟨X,⟩ ∈ M, an elementary submodel of set theory, we define $X_M$ to be X ∩ M with topology generated by $\{U ∩ M: U ∈ ∩ M\}$. Suppose $X_M$ is homeomorphic to the irrationals; must $X = X_M$? We have partial results. We also answer a question of Gruenhage by showing that if $X_M$ is homeomorphic to the “Long Cantor Set”, then $X = X_M$.},
author = {Franklin D. Tall},
journal = {Fundamenta Mathematicae},
keywords = {elementary submodel of set theory; irrationals; reals; Cantor set; Bernstein set; long Cantor set},
language = {eng},
number = {3},
pages = {259-269},
title = {An irrational problem},
url = {http://eudml.org/doc/282913},
volume = {175},
year = {2002},
}

TY - JOUR
AU - Franklin D. Tall
TI - An irrational problem
JO - Fundamenta Mathematicae
PY - 2002
VL - 175
IS - 3
SP - 259
EP - 269
AB - Given a topological space ⟨X,⟩ ∈ M, an elementary submodel of set theory, we define $X_M$ to be X ∩ M with topology generated by ${U ∩ M: U ∈ ∩ M}$. Suppose $X_M$ is homeomorphic to the irrationals; must $X = X_M$? We have partial results. We also answer a question of Gruenhage by showing that if $X_M$ is homeomorphic to the “Long Cantor Set”, then $X = X_M$.
LA - eng
KW - elementary submodel of set theory; irrationals; reals; Cantor set; Bernstein set; long Cantor set
UR - http://eudml.org/doc/282913
ER -