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.

Reference:

Mushaandja, Z. 2009. A quasi-pseudometrizability problem for ordered metric spaces. University of Cape Town.

Mushaandja, Z. (2009). A quasi-pseudometrizability problem for ordered metric spaces. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/4914

Mushaandja, Zechariah. "A quasi-pseudometrizability problem for ordered metric spaces." Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2009. http://hdl.handle.net/11427/4914

Mushaandja Z. A quasi-pseudometrizability problem for ordered metric spaces. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2009 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/4914