Intersection topologies with respect to separable GO-spaces and the countable ordinals

M. Jones¹

¹

Fundamenta Mathematicae, Tome 146 (1994) no. 2, pp. 153-158.

Résumé

Given two topologies, $T_1$ and $T_2$, on the same set X, the intersection topology} with respect to $T_1$ and $T_2$ is the topology with basis ${U_1 ∩ U_2 :U_1 ∈ T_1, U_2 ∈ T_2}$. Equivalently, T is the join of $T_1$ and $T_2$ in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and $ω_1$-compactness in this class of topologies. We demonstrate that the majority of his results generalise to the intersection topology with respect to an arbitrary separable GO-space and $ω_1$, employing a well-behaved second countable subtopology of the separable GO-space.

Détail

DOI : 10.4064/fm-146-2-153-158

Keywords: intersection topology, GO-space, separable, subtopology, normality, $ω_1$-compactness, countable ordinals