Space can be infinitely large. It can also be finitely large. It can also be the three dimensional equivalent of a Mobius strip. That is, have flat curvature, positive curvature, or negative curvature. Thing is, it is impossible to know with absolute certainty.
There are many solutions to possible time travel. For example you could take a black hole, stretch it into a cylinder of infinite length, and make it rotate at the speed of light around it's vertical axis. Boom, time machine. Unfortunately, these sorts of ideas are what some people like to call
Not Even Wrong. In other words, useless to all but the physicists and mathematicians eager to keep their number crunching skill sharp.
As for fractals, they do in fact have infinite surface area around finite volume. This is demonstrable by the fact that you can draw a circle around a fractal, which will have obviously more volume than the fractal that is contained within it.
People who think Fractals have infinite volume have made two errors. The first, is Zeno's Paradox of Achilles and the Tortoise, as has been mentioned before.
http://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise The second involves set theory. Draw a circle. How many points define the edge of the circle? You can always divide the points (mathematically, not physically) down to a smaller number, and thus there are an infinite number of points around the edge of a circle.
Then draw a circle around that circle. It is obvious that one circle is larger, and thus must have more points around it's perimeter, as it encompasses the smaller one, and yet, it also has an infinite number of points on it's perimeter. This is what made the Mathematician Georg Cantor go insane. Inifinity A is demonstrably smaller than Infinity B. The mathematics of Set Theory that he invented goes on to demonstrate that some infinite sets cannot include every item within that set.
Lets say we make an infinitely long list of infinitely long strings of 1's and 0's, and include every possible variation, thus yielding a list like the following
1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . . >
0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . . >
0 1 0 1 0 1 0 1 0 1 0 1 0 1 . . . >
1 0 1 0 1 0 1 0 1 0 1 0 1 0 . . . >
1 1 0 0 1 1 0 0 1 1 0 0 1 1 . . . >
0 0 1 1 0 0 1 1 0 0 1 1 0 0 . . . >
1 1 1 0 0 0 1 1 1 0 0 0 1 1 . . . >
0 0 0 1 1 1 0 0 0 1 1 1 0 0 . . . >
1 0 0 0 1 0 0 0 1 0 0 0 1 0 . . . >
0 1 1 1 0 1 1 1 0 1 1 1 0 1 . . . >
1 0 0 1 0 0 1 0 0 1 0 0 1 0 . . . >
0 1 1 0 1 1 0 1 1 0 1 1 0 1 . . . >
0 0 0 0 1 1 1 1 0 0 0 0 1 1 . . . >
1 1 1 1 0 0 0 0 1 1 1 1 0 0 . . . >
And so on, down the list, and across to the right, forever.
Despite that this list holds every possible combination of 1 and 0, there is one combination of 1 and 0 that it cannot contain. Start at the top left corner, and move diagonally to the bottom right, and highlight ever number like so;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 . . . >
0 0 0 0 0 0 0 0 0 0 0 0 0 0 . . . >
0 1 0 1 0 1 0 1 0 1 0 1 0 1 . . . >
1 0 1 0 1 0 1 0 1 0 1 0 1 0 . . . >
1 1 0 0 1 1 0 0 1 1 0 0 1 1 . . . >
0 0 1 1 0 0 1 1 0 0 1 1 0 0 . . . >
1 1 1 0 0 0 1 1 1 0 0 0 1 1 . . . >
0 0 0 1 1 1 0 0 0 1 1 1 0 0 . . . >
1 0 0 0 1 0 0 0 1 0 0 0 1 0 . . . >
0 1 1 1 0 1 1 1 0 1 1 1 0 1 . . . >
1 0 0 1 0 0 1 0 0 1 0 0 1 0 . . . >
0 1 1 0 1 1 0 1 1 0 1 1 0 1 . . . >
0 0 0 0 1 1 1 1 0 0 0 0 1 1 . . . >
1 1 1 1 0 0 0 0 1 1 1 1 0 0 . . . >
Take this number, and for every every 1, change it to a 0, and for every 0, change it to a 1, yielding:
0 1 1 1 0 1 0 1 0 0 1 0 0 1 . . . >, and so on as we continue across the infinite list. We'll call this the D-number. D for Diagonal.
This number cannot appear anywhere within the infinite list of variations of 1 and 0. Why? Say it were the second number on the list. Since the D-number is the inverse of every number on the diagonal line, the second number would be changed, resulting in a new d-number.
Thus we are literally given infinity + 1.
Tl;dr: Infinity doesn't work that way.