New Non-standard Topologies
نویسنده
چکیده
In this paper, on a non-standard extension (∗X ,∗d) of a metric space (X ,d), we construct a chain of new non-standard topologies in terms of convex subrings of ∗R, its minimal element is the Stopology and its maximal is the Q-topology. Next, we construct X̂ , the F -asymptotic hull of X , and we prove that such space is metrizable and complete when F is generated by an asymptotic scale. Finally, we provide a pseudo-valuation taking integral values, equivalent to the classical Robinson’s valuation, on ρR, the Robinson’s field of ρ-asymptotic numbers.
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