In Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything.

On the other hand, we don't understand the theory too completely, and because of this fuzziness of spacetime, the very concept of spacetime and spacetime dimensions isn't precisely defined.

It's indeed surprising that replacing the elementary particle with a string leads to such a big change in things. I'm tempted to say that it has to do with the fuzziness it introduces.

Edward Witten Quotes