Define metric spaces with examples.

1.	Define metric spaces with examples.
Answer» A metric space is an ordered pair (S, d) where S is a set and d a function on S × S with the properties of a metric, namely: 1. d(x, y) = d(y, x) ≥ 0. 2. d(x, y) = 0 if x = y. 3. The triangle inequality holds: d(x, z) ≤ d(x, y) + d(y, z) for all x, y, z in S.

Answer»

A metric space is an ordered pair (S, d) where S is a set and d a function on S × S with the properties of a metric, namely:

1. d(x, y) = d(y, x) ≥ 0.

2. d(x, y) = 0 if x = y.

3. The triangle inequality holds: d(x, z) ≤ d(x, y) + d(y, z)

for all x, y, z in S.

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Define metric spaces with examples.

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