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Math Help - Topology-Deleted diameter plane

  1. #1
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    Topology-Deleted diameter plane

    Prove that the deleted diameter plane is locally connected and path-connected.


    I've no idea about this question...I'll be delighted to receive some guidance about it...


    Thanks in advance
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  2. #2
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    Quote Originally Posted by WannaBe View Post
    Prove that the deleted diameter plane is locally connected and path-connected.


    I've no idea about this question...I'll be delighted to receive some guidance about it...


    Thanks in advance
    What is your definition of "deleted diameter plane"?
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  3. #3
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    Well, let's define a "deleted diameter circle" to be a circle in R^2 without a finite number of diameters (can be 0... ) but it still contains its center...The deleted diameter plane is the topological space which for every x in R^2 the set of all deleted diameter circles that their center is in x is a neighbourhood base of x...

    Hope you'll be able to help me now because I'm pretty desperate...


    Thanks
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