- Tytuł:
- Intersection topologies with respect to separable GO-spaces and the countable ordinals
- Autorzy:
- Jones, M.
- Tematy:
-
intersection topology
GO-space
separable
subtopology
normality
$ω_1$-compactness
countable ordinals - Pokaż więcej
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Powiązania:
- https://bibliotekanauki.pl/articles/1208416.pdf Link otwiera się w nowym oknie
- Opis:
- 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.
- Dostawca treści:
- Biblioteka Nauki
Artykuł