- #1
1MileCrash
- 1,342
- 41
Hi all,
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?
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?