The unit circle is the elements of F with metric 1, This part below is to help decipher what the question is asking. This is at least the valuation of xt or the valuation of ys or the valuation of st. But usually, I will just say âa metric space Xâ, using the letter dfor the metric unless indicated otherwise. A topological space whose topology can be described by a metric is called metrizable. A set with a metric is called a metric space. Metric Topology -- from Wolfram MathWorld. The open ball around xof radius ", â¦ Thus the valuation of ys is at least v. Use the property of sums to show that Thus the metric on the left is bounded by one of the metrics on the right. The valuation of the sum, A topology induced by the metric g defined on a metric space X. This is usually the case, since G is linearly ordered. Fuzzy topology plays an important role in quantum particle physics and the fuzzy topology induced by a fuzzy metric space was investigated by many authors in the literature; see for example [1â6]. The open sets are all subsets that can be realized as the unions of open balls B(x_0,r)={x in X|g(x_0,x)

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