[Merged by Bors] - feat(Topology): An open cover of a preconnected set has no isolated components#39691
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[Merged by Bors] - feat(Topology): An open cover of a preconnected set has no isolated components#39691Raph-DG wants to merge 4 commits into
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PR summary 0ec643349aImport changes for modified filesNo significant changes to the import graph Import changes for all files
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Co-authored-by: Aaron Liu <aaronliu2008@outlook.com>
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…omponents (#39691) In this PR we show that a family of open sets whose union is preconnected has the property that for any two (nonempty) sets U and V in the cover there is a sequence of sets in the cover U = U_0, U_1,..., U_n = V such that U_i \cap U_{i+1} is nonempty for all i. Co-authored-by: Raph-DG <raphaeldouglasgiles@gmail.com>
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…omponents (leanprover-community#39691) In this PR we show that a family of open sets whose union is preconnected has the property that for any two (nonempty) sets U and V in the cover there is a sequence of sets in the cover U = U_0, U_1,..., U_n = V such that U_i \cap U_{i+1} is nonempty for all i. Co-authored-by: Raph-DG <raphaeldouglasgiles@gmail.com>
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…omponents (leanprover-community#39691) In this PR we show that a family of open sets whose union is preconnected has the property that for any two (nonempty) sets U and V in the cover there is a sequence of sets in the cover U = U_0, U_1,..., U_n = V such that U_i \cap U_{i+1} is nonempty for all i. Co-authored-by: Raph-DG <raphaeldouglasgiles@gmail.com>
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…omponents (leanprover-community#39691) In this PR we show that a family of open sets whose union is preconnected has the property that for any two (nonempty) sets U and V in the cover there is a sequence of sets in the cover U = U_0, U_1,..., U_n = V such that U_i \cap U_{i+1} is nonempty for all i. Co-authored-by: Raph-DG <raphaeldouglasgiles@gmail.com>
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In this PR we show that a family of open sets whose union is preconnected has the property that for any two (nonempty) sets U and V in the cover there is a sequence of sets in the cover U = U_0, U_1,..., U_n = V such that U_i \cap U_{i+1} is nonempty for all i.