I wanted to know if there are any set of characters(and their
corresponding code-points) that remain constant across character
repertoires and encodings.

The '*' character is used for wildcard matching and I wanted to know if
I would be safe in assuming that the code point assigned to this would
remain the same across different encodings as specified by DICOM.

Similarly, are there any other characters(and their code-points) that
would not change across different encodings ?

I would be grateful for any help in this regard.