A quasi-pseudometrizability problem for ordered metric spaces
Doctoral Thesis
2009
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University of Cape Town
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Abstract
In this dissertation we obtain several results in the setting of ordered topological spaces related to the Hanai-Morita-Stone Theorem. The latter says that if f is a closed continuous map of a metric space X onto a topological space Y then the following statements are equivalent: (i) Y satisfies the first countability axiom; (ii) For each y 2 Y, f−1{y} has a compact boundary in X; (iii) Y is metrizable. A partial analogue of the above theorem for ordered topological spaces is herein obtained.
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Includes abstract.
Includes bibliographical references (leaves 83-88).
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Mushaandja, Z. 2009. A quasi-pseudometrizability problem for ordered metric spaces. University of Cape Town.