Asymmetric Topology and Its Applications in Areas of Computer Science - Orinda, Abraham;Gaba, Yaé;Amburo, Collins
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Metrics provide an abstract setting which unifies through axioms the common properties of distances in different contexts. An overarching and a more general concept of continuity becomes possible to define with metric spaces. It is also known that metrics are naturally Hausdorff. The Hausdorff property however loses the partial ordering inherent in $T_0$ spaces, and hence superfluous under Scott's topology. Problems arising in areas of computer science such as denotational semantics and complexity analysis therefore ratified the need to propose metric space generalizations that could be used…mehr

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Produktbeschreibung
Metrics provide an abstract setting which unifies through axioms the common properties of distances in different contexts. An overarching and a more general concept of continuity becomes possible to define with metric spaces. It is also known that metrics are naturally Hausdorff. The Hausdorff property however loses the partial ordering inherent in $T_0$ spaces, and hence superfluous under Scott's topology. Problems arising in areas of computer science such as denotational semantics and complexity analysis therefore ratified the need to propose metric space generalizations that could be used to define non-Hausdorff topologies. The need for the generalization however pays the price of losing the nicer properties associated with the Hausdorff property. Here, we look into the possibility of weakening to a maximum the imposed conditions required of a self mapping in the postulation of Kleene's fixed point theorem in order to guarantee a fixed point, when the underlying partially ordered set comes from a $T_0$-quasi-metric space. Ultimately, we apply the weakened fixed point technique in asymptotic complexity analysis of algorithms whose running time follows a recurrence equation.
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Autorenporträt
Abraham is a passionate young man with profound interest in Pure Mathematics. A firm believer in hope--a leap of faith keen on using Mathematics to suggest solutions beneficial to societies. I obtained my MSc in Mathematics from the University of Cape Town and African Institute of Mathematical Sciences.