Random Question During Cookie-Baking

Is it interesting to study the topology of fractal objects like the Sierpinski carpet? Given that they tend to be "mostly holes" rather than a nice* "surface" per se.

I actually don't know any topology, unfortunately, so my question might be a really dumb one. Oh well.

Anyway, I thought about this because I was making Sierpinski cookies (3 iterations, where a plain square is the 0th iteration) and they turned out kind of deformed. Ok, really deformed. However, I can probably say that the cookies (before I bake them) can be continuously un-deformed into the (3rd iteration) Sierpinski carpet. Idly wondering whether I'd actually be correct in saying that led to the actual question posed at the beginning of this post.

*"Nice" means alot of things in my lexicon. I usually use it with functions, where it means definitely at least continuous, probably C¹ (or even smooth, maybe analytic, though I don't use these conditions much yet), possibly with nonzero derivative everywhere if the function's C¹. For a surface I'll parametrize it (if possible) then apply my definition of "nice" for functions (if there exists more than one parametrization I guess I'll pick the "canonical" one if it exists, or just "the nicest one I know for my current purposes" if there's no obvious choice). For a subset in a metric space I guess I want it to be compact and connected (it's been awhile since real analysis).