I am not aware of GR, but due to curiosity i have a question in my mind. Please let me know if it is inappropriate to ask here.
My question is about singularity. I am under the assumption that singularity means in mathematical terms equivalent to a discontinuity in a function. My question is what type of discontinuity are the ones corresponding to Penrose-Hawking singularity theorems and also to the the naked singularity ? by type i mean
removable (left and right limits exist and are equal but not equal to the function value at that point).
a jump type discontinuity (left and right limits exists and are not equal to each other).
Oscillating discontinuity (as described as described in the above given link)