[c] How does one represent the empty char?

Yes, c[i]='' is not a valid code. We parenthesis character constant between ' ', e.g. c[i] = 'A'; char A. but you don't write any char in between ''.

Empty space is nothing but suppose if you wants to assigned space then do:

c[i] = ' ';
//      ^  space 

if wants to assigned nul char then do:

c[i] = '\0';
//       ^ null symbol 

Example: Suppose if c[] a string (nul \0 terminated char array) if you having a string. for example:

char c[10] = {'a', '2', 'c', '\0'};

And you replace second char with space:

c[1] = ' ';

and if you print it using printf as follows:

printf("\n c: %s", c);

then output would be:

  c:  a  c
//      ^ space printed 

And you replace second char with '\0':

c[1] = '\0';

then output would be:

  c:  a

because string terminated with \0.