A quasi-pseudometrizability problem for ordered metric spaces

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.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2009

Author dc:creator

• Mushaandja, Zechariah

Advisor dc:contributor.advisor

• Künzi, Hans-Peter A

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/4914

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/4914