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

• Autorzy: M. R. Jones
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

intersection topology; GO-space; separable; subtopology; normality; $ω_1$-compactness; countable ordinals

Kategorie tematyczne

• 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
• 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994-1995
• Tom: 146
• Numer: 2
• Strony: 153-158

Daty

wydano

1995

otrzymano

1993-09-13

poprawiono

1994-04-27

Twórcy

autor

M. R. Jones

• St. Cross College, University of Oxford, Oxford OX1 3LZ, U.K.

Bibliografia

• [1] M. R. Jones, Sorgenfrey-$ω_1$ intersection topologies, preprint, 1993.
• [2] J. L. Kelley, General Topology, Springer, New York, 1975.
• [3] K. Kunen, On ordinal-metric intersection topologies, Topology Appl. 22 (1986), 315-319.
• [4] A. J. Ostaszewski, A characterisation of compact, separable, ordered spaces, J. London Math. Soc. 7 (1974), 758-760.
• [5] G. M. Reed, The intersection topology with respect to the real line and the countable ordinals, Trans. Amer. Math. Soc. 297 (1986), 509-520.