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Recently I was working on systems of subsets satisfying the following properties

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Obviously, it is just useful partitioning for further magic but I wonder if there is some theoretical treatment of such systems. Any suggestion for reading is welcome

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  • $\begingroup$ $4$ is not really a property, rather a definition of more variables... $\endgroup$ Jun 21, 2021 at 13:15
  • $\begingroup$ It would improve your Question to highlight early on that $S$ is a topological space. $\endgroup$
    – hardmath
    Jun 21, 2021 at 17:59
  • $\begingroup$ What is $\Sigma$ supposed to be? . $\endgroup$ Jun 21, 2021 at 22:36
  • $\begingroup$ There is a relation between this and a thing called a Partition Of Unity. $\endgroup$ Jun 21, 2021 at 22:49
  • $\begingroup$ $\Sigma$ should be switchning manifold. In fact, this partition comes from piece-wise smooth ODEs $\endgroup$
    – struct
    Jun 22, 2021 at 8:36

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