Abstract
We give an internal characterization of the notion of zero-dimensionality in preordered topological spaces. It is shown that for compact partially ordered topological spaces this property is equivalent to total order-disconnectedness. We define the notion of strong zero-dimensionality in preordered topological spaces and give several internal characterizations.
A draft of this paper was written at the University of Cape Town (UCT) in December 1993 using the results from the author’s M.Sc. thesis (UCT 1993, produced under the supervision of Professor G. C. L. Brummer). Grants from the Foundation for Research Development and from UCT via the Topology and Category Theory Research Group are acknowledged.
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Nailana, K.R. (2000). (Strongly) Zero-Dimensional Partially Ordered Spaces. In: Brümmer, G., Gilmour, C. (eds) Papers in Honour of Bernhard Banaschewski. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2529-3_27
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DOI: https://doi.org/10.1007/978-94-017-2529-3_27
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