Question

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

Answer 1

@zzr0ck3r

Answer 2

is it 2?

Answer 3

@zzr0ck3r

Answer 4

it should be 2

Answer 5

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 \(A\cap (B-\{2\})=\emptyset\)

Answer 6

ok. so which are the limit points sir?