Is every GO-topology a join of two orderable topologies?

Authors:
Paul R. Meyer, Victor Neumann Lara and Richard G. Wilson

Journal:
Proc. Amer. Math. Soc. **84** (1982), 291-296

MSC:
Primary 54F05

DOI:
https://doi.org/10.1090/S0002-9939-1982-0637186-9

MathSciNet review:
637186

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Abstract: As a generalization of -topologies ( ), we are interested in those topologies (here called -topologies) on a set which can be expressed as a join of orderable topologies (the join being taken in the lattice of all topologies on ). If a topology is the join of orderable topologies we say is . It is not difficult to prove that every -topology is a -topology, but the question (raised in [**M 71**]) as to whether every -topology is seems much more difficult). We show that is if is a subspace of an orderable space , where is either metrizable and locally separable, or connected with countable cellularity. (The theorem is actually more general than is stated here.) We give an example to show that for any positive integer there is a finite join of order topologies which is not , but these are not -topologies.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1982-0637186-9

Keywords:
Orderable topology (LOTS),
generalized order topology ( -topology, suborderable topology),
lattice of topologies,
join of topologies

Article copyright:
© Copyright 1982
American Mathematical Society