I am little bit stumped by this proof.

> 
> Show that $(a,b), a < b$ and $ a, b \in \mathbb{R}$ is open in the usual topology of $\mathbb{R}$ and $[a,b)$ is not
> 
> 
> 

Recall that the usual topology on $\mathbb{R}$ is 

$$\tau\_u = \{U \subseteq \mathbb{R} | \forall x \in U, \exists \delta > 0, \text{ s.t. }(x-\delta, x+\delta) \subseteq U\}$$ 

The part for $[a,b)$ is trivial, we can pick $x = a$, then the conclusion follows.

But how do I show that $\forall x \in (a,b), \exists \delta > 0$? Can someone provide a starting point or a sketch?