Generating a subbasis from a Topology

I know that given a subbasis, a topology could be generated by taking all unions of finite intersections of the elements of the subbasis. I also know that given a topology, one could generate a basis. My question is, is there a way to generate a subbasis when one is given a topology?

• You can consider the topology itself. Or that basis you are referring to. – user228113 Apr 19 '18 at 9:32
• Ah, I see now. Then is there more than one way to get a subbasis from a topology? – SKYejin Apr 19 '18 at 9:34
• At least as many as there are of selecting a basis. – user228113 Apr 19 '18 at 9:34
• There is no "easy way" to find a subbase with a special property, e.g. supercompact spaces have a special subbase wrt open covers. Every compact metric space has such a subbase, but it's not always obvious how to find it. – Henno Brandsma Apr 19 '18 at 22:01