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My Topology textbook arrived in the mail today, so I started reading it. It begins with an introduction to an object called metric spaces.

It says

A metric on a set X is a function d: X x X -> R that satisfies the following conditions:

-some conditions--

I am not completely sure about this notation (mainly the "d:" part.) I believe that X x X is simply the Cartesian product. My guess is that d is the function's name, and the rest just says the domain of this function in relation to the set X (kinda?)

So is it correct to read it in this way: d: X x X -> R

Means:

Some function d, of x and y, where x and y refer to axis of a 2d plane. This 2d plane is the cartesian product of the set X and itself.

So if X were the set {1,2,3}, this notation defines d to be a function of x and y such that either x or y is equal to 1, 2, or 3?

Or is this not right?