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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?

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    $\begingroup$ You can consider the topology itself. Or that basis you are referring to. $\endgroup$ – user228113 Apr 19 '18 at 9:32
  • $\begingroup$ Ah, I see now. Then is there more than one way to get a subbasis from a topology? $\endgroup$ – SKYejin Apr 19 '18 at 9:34
  • $\begingroup$ At least as many as there are of selecting a basis. $\endgroup$ – user228113 Apr 19 '18 at 9:34
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    $\begingroup$ 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. $\endgroup$ – Henno Brandsma Apr 19 '18 at 22:01

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