TheTopology on the real line R generated by left open right closed interval $(a,b]$ is
Choose the correct option
$a)$ strictly coarser than the usual topology
$b)$ strictly finer than the usual topology
$c)$ NOT comparable with usual Topology
$d)$ same as the usual Topology
My attempts : I thinks option $b)$ will correct because
$$
(a,b) = \cup_{n\ge 1} \ (a ,b+\frac{\epsilon}{n}]
$$
where $\epsilon < \frac{b-a}{2}$
This implies $(0,1]$ is not open in the usual topology.
is Its correct??
Best Answer
Yes, it is correct. How about $[a,b)$ ?Is it the same ?also there are many typologies that finer and coarser than the usual topology