Can a fractal be a manifold? if so: will its boundary (if exists) be strictly one dimension lower?

So it is weekend! and I am reading a nice book, "The Poincaré conjecture", written by a mathematician (Donal O'Shea, topologist). The book introduces step by step basic concepts of Topology, and talks about the mathematical advances since Poincaré stated the conjecture up to the moment it was demonstrated, providing a glimpse of the solution that Perelman gave to the conjecture. It is not technical, narrative, a very light reading.

My question is about the following: when the author defines a manifold, states that "if a manifold has a boundary, its boundary will be one dimension lower".

Then I thought about fractals, for instance: can a fractal be a manifold? (I understand that manifold means the same as "surface" in this context) and then, if the answer is yes, then if it has boundaries, are the boundaries strictly one dimension lower?

My beginner doubt is basically if the statement of the author would be still valid in that case. Maybe I am confusing the "fractal dimension" concept with the generic "dimension" concept.

Thank you!

UPDATE 2015/08/28

There is a very nice follow-up on this question, with an interesting explanation as well by another user here (link).

If you mean a set whose fractional Hausdorff measure is finite and non-zero, then this will not be a manifold. But it will have a topological boundary. That won't be a manifold boundary because it isn't a manifold. Not in the usual sense of the word "manifold" anyway.