The Sup Metric on Infinite Products
نویسنده
چکیده
Of all the equivalent metrics in Euclidean spaces, the sup metric is the one which can immediately be extended to infinite products of real lines. Nonetheless, it appears that no one has investigated the properties of this metric; since we could not think of any good reason for this, we decided to have a go at it and, in our opinion, the results which follow show that this metric is useful. Many pertinent questions remain open. We conclude this study by introducing the sup uniformity in infinite products of uniform spaces; however, we know very little about its properties.
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