# Do modules have any topology?

Is there any kind of topology, natural or unnatural, that modules do have? Is there any geometric interpretation for flat modules? Is "exactness" of a sequence, any kind of geometric condition? Thanks.

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Sure: every module carries the discrete topology, and also the indiscrete topology. But this is not a particularly useful observation. –  Qiaochu Yuan Mar 25 '12 at 21:11
the Krull-toplogy, see en.wikipedia.org/wiki/Completion_(ring_theory –  Blah Mar 25 '12 at 21:11
@QiaochuYuan surely, but any kind of interesting topology, I mean, not the trivial one. –  Jr. Mar 25 '12 at 21:36