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I crossed with the Kuratowski closure-complement theorem while learning Munkres's Topology (Problem 21 in Section 17; Page 102, 2nd edition). The following description is from B.J. Gardner and M. Jackson.

The Kuratowski Closure-Complement Theorem: If $(X, \tau)$ is a topological space and $A \subseteq X$ then at most 14 sets can be obtained from $A$ by taking closures and complements.

As stated in B.J. Gardner and M. Jackson, this remarkable theorem and related phenomena have been the concern of many authors. However, being not a researcher in Topology,

My Problem: I would expect to see more interesting applications of the Kuratowski theorem in other fields, even in some non-mathematical fields (such as computer science).

I failed to find related literatures through googling.

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A comprehensive bibliography through 2012 on this subject can be found at www.mathtransit.com. References are listed in chronological order. –  mathematrucker Jan 22 at 14:20
    
@mathematrucker Thanks. For me, however, the resources are still theories focusing on topology/algebra rather than applications in other fields. (I have just scanned through this list.) –  hengxin Jan 28 at 2:37
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Though not "applications", these two papers are close to computer science: Complements and Transitive Closures, The Fast Skew-Closure Algorithm. This 1994 talk may actually qualify as suggesting an application, in a (very) non-mathematical field: Topological Foundations of Cognitive Science –  mathematrucker Jan 29 at 17:26

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