2let xab 1 can you make x a metric space 2If the answer is y

2.let x={a,b}

1) can you make x a metric space?

2)If the answer is \'yes\', can you make x a metric space in more then one way?

3)How many ways can you make x a metric space?

Solution

Matric space : a matric space is an ordered pair (A, B) where a is a set and B is a matric

And B defined B: A*A---->R

R is real number

And matric space holds following conditions

Nonnegative, identity, symmetry and sub additivity

Given x ={a, b}

For matric space first two conditions satisfies.

But symmetry and sub additivity not satisfied because these two conditions required three variables

But given two variables only

There fore we can not make matric space