Based on certain intuitions and motivations we make certain definitions and then proceed to use these concepts in further developing our intuition. For example, we have an intuition that a line has dimension one, a plane dimension two and so on. Hence when we define the term dimension, it is in such a manner that it matches with our natural feeling, whether that is in the area of topology or vector spaces or inner product spaces.
Now, very often it could turn out that the definition seems to include non-intuitive cases. For example a space filling curve does not match with the natural feeling of a curve, even though it is a continuous map as required by the definition of the curve.
My question is are there any examples in which the terms involved have been redefined because it was found that the previous definitions are inadequate?