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Math Help - path connectedness

  1. #1
    Junior Member
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    path connectedness

    This is a pretty trivial question (I think?). I just want to see anyone do it with a bit of detail to determine if I am on the right track. thanks!

    Let X={a,b} and assume that X has the topology T={0, {a},X}. Show that X is path connected in this topology.
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  2. #2
    Senior Member JaneBennet's Avatar
    Joined
    Dec 2007
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    Try the map p:[0,1]\to X, p(t)=a if t\ne1 and p(1)=b.

    Then p^{-1}(\O)=\O, p^{-1}(\{a\})=[0,\,1), p^{-1}(X)=[0,\,1] which are all open in [0,\,1].
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