general-topology
I need to build a topology with $ X = \{a,b,c,d,e,f \} $ but I have very clear how?
there are so many elements.
I know the properties of topological spaces, but not how
anyone know how?
is not well identify sets that can give me a topology.
I tried with:
$\{X,\{a\},\{b\},\{c\}\}$ and $\{X,\emptyset\}$ but I don't know.
What is the minimal topology of $X$?
I will try to answer the question I think you should have asked instead. This should perhaps be a coment instead but it is too long.
Take the union of all the walls in a portal level. This is an orientable two-dimensional manifold $M$. The set of points the player can occupy is some connected component $C$ of the complement of the manifold in $\mathbb R^3$. Let $D$ be the complement of $C$. If we assume there are no "floating walls" in the level, then $M$ is a (connected) orientable compact surface without boundary. Due to the classification of closed surfaces, $M$ has a genus $g\geq 0$, so it is homeomorphic to a sphere with $g$ handles. Identifying two discs on $M$ is equivalent to adding another handle to the surface. You can picture it by just digging a tunnel inside $D$ between the two discs. It will look something like this: 
I got the picture from this Wikipedia page, which has two more representations of the same surface.
Now, it remains to deal with the case of shooting one portal on a wall and another on a floating platform. In this case you can't dig a tunnel inside $D$ between the portals since $D$ is not connected. We could however embed $C\subseteq \mathbb R^3$ in $\mathbb R^4$, and dig a tunnel between the portals inside $\mathbb R^4-C$, but now we have a space embedded in $\mathbb R^4$, which of course more difficult to picture. Thus the general case of a portal level is the union of a finite number of spheres with handles, where portals connecting different wall components are realized by tunnels extending into a fourth dimension. I don't know if there's a simpler way to describe this.
Any indiscrete space is perfectly normal (disjoint closed sets can be separated by a continuous real-valued function) vacuously since there don't exist disjoint closed sets. But on the other hand, the only T0 indiscrete spaces are the empty set and the singleton.
Only the empty and singleton indiscrete spaces are metrizable, but every indiscrete space is compatible with the pseudometric $d(x,y)=0$ for all $x,y$.
Any indiscrete space is compact since its only open cover is finite to begin with ($\{X\}$).
Every basis for an indiscrete space is finite ($\Rightarrow$ countable), so it is second-countable and therefore separable.
$X$ is the only nonempty clopen set, so indiscrete spaces are connected. They are also:
Best Answer
The properties of a topology $\tau$ on a space $X$ are as follows:
In your first example you have $\{a\} \in \tau$ and $\{b\} \in \tau$, but their union, $\{a, b\}$ is not in $\tau$. therefore this cannot be a topology.
Your second example $\tau = \{X, \emptyset\}$ will be a topology for any space $X$. It is the simplest topology allowed, and it is therefore called the trivial topology.
The following topology also has a name: $\tau = \{U \mid U \subseteq X\}$, containing all subsets of $X$. It is called the discrete topology. Another valid topology is $\tau = \{\emptyset\} \cup \{U \mid a \in U\}$ where a set is open iff it contains $a$ or is the empty set.
All in all there are a lot of different topologies on your $X$. If you want to make your own example, do this: Start with a few subsets, containing $X$ and $\emptyset$ (this starting point is called a sub-basis for the resulting topology). Now add to your collection all possible intersections of your sets (only intersections between finitely many sets are allowed, but that makes little difference when the set itself is finite) (what you now have is called a basis for the topology you end up with). Then append all possible unions of those sets again. You now have a full-fledged topology on your space.