## anonymous one year ago Let A=(0,1]⋃2 be a subset of R . Then the isolated points of A in R is

1. anonymous

@zzr0ck3r

2. anonymous

is it 2?

3. anonymous

@zzr0ck3r

4. anonymous

it should be 2

5. zzr0ck3r

Yes it is 2, proof: Let $$x\in (0,1]$$. Then for all intervals $$(a,b)$$ containing $$x$$ we have $$(a,b)\cap [(0,1]-\{x\}]\ne \emptyset$$. Now consider $$B=(1.5,27)$$. Surely this is open and contains $$2$$ and $$A\cap (B-\{2\})=\emptyset$$

6. anonymous

ok. so which are the limit points sir?