Re: relative topology in R^2

>> Sure. First of all, what does the phrase 'relative topology'
>> mean? What will be a base for the relative topologies on
>> those sets? After considering that question, you may want to look
>> at intersections of your sets A and B with elements of your
>> original base. Drawing a picture may help.
>> 
>>  What does it mean to be the discrete topology? What are the
>> smallest sets you can get to be open in A? What type of sets 
>> are basis sets for B?
>> 
>> --Dan Grubb

>I can see that I have to show there is open singleton set in Base/\A.
>But Base/\A = {(x,-x) | a<=x<b, -b<-x<=-a}

Not quite. The base elements are {(x,y):a<=x<b,c<=y<d}. If you have
a point (r,-r) in A, can you find a basis element that only
intersects A in that one point? Hint: Draw a picture.

>I don't know how to extract singleton set from this set.
>Is (a,-a) a singleton set we are looking for?

--Dan Grubb