I am reading the paper Pratulananda Das and Ekrem Savas: [On I-convergence of nets in locally solid Riesz spaces](http://www.doiserbia.nb.rs/img/doi/0354-5180/2013/0354-51801301089D.pdf), Filomat 27:1 (2013), 89–94, [DOI: 10.2298/FIL1301089D](http://dx.doi.org/10.2298/FIL1301089D).

I am stuck at example $3.2$ 

Here is how far I managed :

Conferring the definitions in p.g.$90$, we have, for a net $\{s\_{\alpha}:\alpha \in D\}$ where $D$ is directed set and $s:D\rightarrow X$ is the net. $$D\_{\alpha}=\{\beta \in D : \beta \ge \alpha\}\\F\_{0}=\{ A\subset D : A\supset D\_{\alpha} \text{ for some }\alpha \in D\}\\I\_0=\{ A\subset D : A^c \in F\_0\}$$ 
 $N\_{x\_{0}}$ is the nbd system of a fixed point $x\_0$ forming a directed set under inclusion. So I take it that means $A\lt B$ iff $A\subset B.$ Then $D\_{A}=\{ \text{nbd's of }x\_0 \text{
that contains A}\}.$ And $$I\_0=\{ A\subset D : A^c \in F\_0\}\\=\{ A\subset D : A^c \supset D\_{B}\text{ for some }B\in D\}\\=\{ A\subset D : A\subset D\_B \text{ for some } B\in D\}\\=\{ A\subset D : A\supset B \text{ for some nbd B of } x\_0 \}$$ 
 Now for any ideal $I$ of $D$ that contains $I\_0$ , if $C\in I\backslash I\_0.$ Then $$C=\{ A\subset D : \text{there is some nbd B of }x\_0 \text{ such that }A \text{ does not contain B}\}$$

And the net $\{ s\_U\}$ is given by 
$$s\_U\in I ,\forall U\in N\_{x\_0}\backslash C\\ s\_U= y\_0 \forall U \in C,\text{ where } y\_0 \neq x\_0 \text{ is a fixed point. }$$

Then we can easily see that $\{s\_U\}$ cannot converge to $x\_0$ usually. Because of Hausdorff property we can find disjoint nbd's of $x$ and $y$. And for $U\in C$ $s\_U=y\_0$ won't be in the nbd of $x\_0.$ And we will find infinitely manu such $s\_U$'s.

The next thing is to prove it is $I\_{\tau}$ convergent. I could not do this at all for I could not comprehend the given equation $$\{ U\in D : s\_U- x\_0 \lt U\}=C\in I.$$ 

Help me with this. Also , if there is any mistake in what I have done above , please point out. Thanks.