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    Components of excluded-point and included-point real lines

    P-UNL871F13-PS7.3BC

    Area
    Topology
    Topics
    Connectedness
    Status
    draft
    Contents

    For each of the following topologies on the underlying set \(\mathbb R\), determine whether the resulting space is connected or path-connected, and determine its connected components and path components.

    1. The excluded-point topology (with excluded point \(0\)).

    2. The included-point topology (with included point \(0\)).

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