The Topology on the real line R generated by left open right closed interval $(a,b]$ is Choose the correct option

Question

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??

Answer 1

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