[AntonioLao]

the validity of a theory of limit make the Menger sponge, Sierpinski carpet and Koch curve realizable.

Is the universe a certain type of Menger sponge?

[AntonioLao]

for information about Menger sponge see
http://mathworld.wolfram.com/MengerSponge.html

[Guille]

If the universe is one of these menger sponge, then what would these "holes" be? where would the lead?

I have my own answer to my questions, but I want to see others:

1) the holes are black holes

2) the lead to the other side of the singularity: another universe

[AntonioLao]

Originally Posted by GUILLE 1) the holes are black holes

what do you think is the physical dimension of each hole?

[Guille]

Originally Posted by AntonioLao what do you think is the physical dimension of each hole?

well,

the black holes (this is what I have deducted) are four dimensional. But the holes aren't actually the black holes themselves, but the holes are the singularities, the very end of the black holes, which (of what I know) is zero dimensional. isn't it?

[AntonioLao]

Originally Posted by GUILLE the very end of the black holes, which (of what I know) is zero dimensional. isn't it?

but singularity cannot exist because there is no plausible explanation for an evolution out of this singularity. My hypothesis is that the holes are one dimensional, and while for superstring theorists, they believed the holes are six dimensional plus the 4D of spacetime total 11-dimensional.

[Guille]

Originally Posted by AntonioLao but singularity cannot exist because there is no plausible explanation for an evolution out of this singularity. My hypothesis is that the holes are one dimensional, and while for superstring theorists, they believed the holes are six dimensional plus the 4D of spacetime total 11-dimensional.

then, the holes can't be squares (as shown in the link you gave).

[AntonioLao]

Because the topological equivalent of all one-dimensional objects can be found in a Menger sponge, it can be used as a mathematical model of spacetime structures at the infinitesimal region of spacetime. But once LIM is implied then two distinct topologies can be isolated.