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Studies on ultraquasi-pseudometrics and orderings
Ultraquasi-pseudometric spaces even though quite simple in concept, as it is easily obtained by altering the usual triangle inequality property, still yield interesting results. Indeed, a natural question that should arise is how does switching to the strong triangle inequality affect some of the re...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2018
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| Summary: | Ultraquasi-pseudometric spaces even though quite simple in concept, as it is easily obtained by altering the usual triangle inequality property, still yield interesting results. Indeed, a natural question that should arise is how does switching to the strong triangle inequality affect some of the results we already know about quasi-pseudometrics. On some points we get similar results to those of when we have the standard triangle inequality, but the general observation is that dealing with the strong triangle inequality is easier. Of course, there are results that cannot be obtained without the "ultra-property". A fast rundown on those effects is then deemed necessary to begin with. Also, since we cannot go through every single result on quasi-pseudometrics we then need to localize our observations, that is why in the first part we restrained our observations on the results from Gaba and Künzi about splitting metrics. Also, we will see some particular algorithms and connections to the bicompletion, joincompact ultraquasi-metric spaces and the old construction of a total order by Herrlich. |
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