An irrational problem

Franklin D. Tall¹

¹ Department of Mathematics University of Toronto Toronto, Ontario M5S 3G3, Canada

Fundamenta Mathematicae, Tome 175 (2002) no. 3, pp. 259-269

Résumé

Given a topological space $\langle X , {\cal T}\rangle \in M$, an elementary submodel of set theory, we define $X_M$ to be $X\cap M$ with topology generated by $\{ U \cap M : U \in {\cal T} \cap M \}$. 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 $X= X_M$.

Détail

DOI : 10.4064/fm175-3-3

Keywords: given topological space langle cal rangle elementary submodel set theory define cap topology generated cap cal cap suppose homeomorphic irrationals have partial results answer question gruenhage showing homeomorphic long cantor set