QUOTIENT SPACE TOPOLOGY

[ganeshsree86]

Consider the equivalence relation on R^2 defined by (x1,x2) ~ (w1,w2) if x1+x2 = w1+w2. Describe the quotient space that results from the partition of R^2 into the equivalence classes in this equivalence relation.
Can anyone help me with this question? Have no idea where to even begin!!! Pls help.
Thanks!

oops...sorry forgot to define R^2. R^2 is the real euclidean plane. thanks again guys. :wink:

Cheers,
Ganeshsree

 

[daon]

To get an idea, pick a point, say (1,1) and find what is identified with it.

[(1,1)] ={ (x,y); x+y=2} i.e the points on the line y=-x+2 (interecept 2 and slope -1)

What can you say then about [(a,b)]?

 

[ganeshsree86]

HELLO....thanks a lot for the reply...i managed to obtain the equivalence classes but i don't know how to describe the quotient space that results from the partition of R^2 into those equivalence classes....in fact i don't know how to partition R^2 into those equivalence classes so that a quotient space will be formed.
Hope someone can help me...Thanks in advance guys!!!

Cheers,
Ganeshsree