Abstract
Let X be a set. We say that X is a metric space if there is a nonnegative function ϱ of two arguments, defined on X, ϱ(x, y) ≥ 0, x, y ∈ X, and called a metric, which satisfies the following conditions:
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(1)
ϱ(x, y) = 0 if and only if x = y
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(2)
ϱ(x, y) = ϱ(y, x)
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(2)
ϱ(x, y) ≤ ϱ(x, z) + ϱ(z, y) (triangle inequality).
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© 1987 Springer Science+Business Media Dordrecht
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Rolewicz, S. (1987). Metric spaces. In: Functional Analysis and Control Theory. Mathematics and its Applications, vol 29. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7758-8_1
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DOI: https://doi.org/10.1007/978-94-015-7758-8_1
Publisher Name: Springer, Dordrecht
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