Q:

Freddy Krueger's Lullaby

1, 2.
Freddy is drawing eyeballs.
2½, 3.
One iris got bigger.
3½, 4.
The other got bigger.
5, 6.
Aura passes from and to irises.
[NUMBERS REDACTED]
Never sleep again.

What is Freddy singing about?
Subtle Hint:

 Start with dots.

Moderate Hint:

 The numbers are redacted because currently, numbers end by 6.

Decisive Hint:

 The "aura" may seem like equipotentials between heterogeneously charged conductors:

 

A:

He is singing about

 The separation axioms.

1, 2. Freddy is drawing eyeballs.

 In $T_2$ spaces, or Hausdorff spaces, every two distinct points can be seperated by open sets. It is commonly depicted by the following diagram: 

2½, 3. One iris got bigger.

 In $T_3$ spaces, or regular spaces, every disjoint closed set and point can be seperated by open sets. It is commonly depicted by the following diagram:

3½, 4. The other got bigger.

 In $T_4$ spaces, or normal spaces, every two disjoint closed sets can be seperated by open sets. It is commonly depicted by the following diagram:

5, 6. Aura passes from and to irises.

 In $T_6$ spaces, or perfectly normal spaces, for every two disjoint closed sets, there exists a continuous function whose return value is 0 on and only on one closed set and 1 on and only on the other closed set. (Hence the decisive hint)

