My recent research into the theory of order topology led me to realize just how connected the theory of order topology and metric spaces is. A metric space can be partially characterized by the order topology of its distances, so that a metric space with discrete distances is itself discrete. In this way, order topology is connected not only to the theory of metric spaces but all of mathematical analysis. The results of this research, and a considerable examination of the theory of total orders in general is presented in the following paper.
https://drive.google.com/file/d/1RNg0yXtIad6ziTvjkzINajBknPl6n9wG/view?usp=sharing
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