A quasi-pseudometrizability problem for ordered metric spaces

Includes abstract.Includes bibliographical references (leaves 83-88).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

Local connectedness of frames

In this thesis, we undertake a systematic study of local connectedness of frames. Among other central ideas in this study is that of a connected congruence on a frame. We show that the two definitions of a connected congruence in literature (section 2.2) are not equivalent, and hence introduce a new term for one of them. We also prove that, using Baboolal's methods, if the Stone-Cech compactification βL is locally connected then L need not be locally connected for completely regular frame L. This happens in chapter 5

Incorporating Video Game Music into Music Education: Potential Benefits and Challenges

This study examines the potential benefits of incorporating video game music into various forms of music education. Since no previous scholarly work could be found on this specific subject, this study relies on examining various aspects of video game music and adjacent studies on student motivation and achievement. The study is broken up into several sections. An analytical study determines that video game music has developed to the point where it is just as complex as other forms of music and has unique aspects that could make it a valuable tool in education. The study also examines the uses of music in games in terms of narrative and producing desired feelings and emotions. This section provides ample evidence that video game music provides unique and compelling examples of practical uses of music in media. The third and final section explores scholarly work incorporating student’s interests into education. Overall, there is a strong case for video game music gaining more representation in education, but gathering solid proof would require larger and longer-term studies than this project\u27s scope