I want to make a function which checks a string for occurrences of other strings within them.
However, the sub-strings which are being checked may be interrupted within the main string by other letters.

For instance:

a = 'abcde'
b = 'ace'
c = 'acb'

The function in question should return as b being in a, but not c.

I've tried set(a). intersection(set(b)) already, and my problem with that is that it returns c as being in a.

You can turn your expected sequence into a regex:

import redef sequence_in(s1, s2):"""Does `s1` appear in sequence in `s2`?"""pat = ".*".join(s1)if re.search(pat, s2):return Truereturn False# or, more compactly:
def sequence_in(s1, s2):"""Does `s1` appear in sequence in `s2`?"""return bool(re.search(".*".join(s1), s2))a = 'abcde' 
b = 'ace' 
c = 'acb'assert sequence_in(b, a)
assert not sequence_in(c, a)

"ace" gets turned into the regex "a.*c.*e", which finds those three characters in sequence, with possible intervening characters.