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    I have in the complex plane the set B with
    B={z:im z<=0 and 2<=|Z-1|<3}

    and im also asked to consider the boundary of B and say if they are a region or not.

    I think that both sets are not open and connected so not regions but the way questions run in this course I think one should be a region and one should not.

    it must be the deciding which set is open im getting wrong. all im needing to say, according to the course notes is B includes a boundary point,eg, any point on the circumference of the circle of radius 3 and having imaginary part <0.

    likewise I think the boundary of B is not open.
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    (Original post by mathz)
    I have in the complex plane the set B with
    B={z:im z<=0 and 2<=|Z-1|<3}

    and im also asked to consider the boundary of B and say if they are a region or not.

    I think that both sets are not open and connected so not regions but the way questions run in this course I think one should be a region and one should not.

    it must be the deciding which set is open im getting wrong. all im needing to say, according to the course notes is B includes a boundary point,eg, any point on the circumference of the circle of radius 3 and having imaginary part <0.

    likewise I think the boundary of B is not open.
    It's somewhat difficult to make out what you're saying there.

    You mention both sets, but there is only one, unless you are considering:

    {z:\im z\leq 0} and {z: 2<=|Z-1|<3}

    as two separate sets.

    That said, neither of those is open, nor is your set B

    If your requirement for a region is that the set is open, then no, they're not regions.

    For B, the boundary does not include the circle of radius 3, however it does include the circle of radius 2. So any point on there with Im(z) < 0 will serve as your boundary point.
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    Sorry for being vague.

    The 2 sets I meant were B and the boundary of B.

    The set B is all z with z inbetween the 2 circles and having Im(z)<0
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    (Original post by mathz)
    Sorry for being vague.

    The 2 sets I meant were B and the boundary of B.

    The set B is all z with z inbetween the 2 circles and having Im(z)<0
    Must have had a mental aberration yesterday - your post reads fine when I look at it today.

    What's your definition of a region?
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    (Original post by ghostwalker)
    Must have had a mental aberration yesterday - your post reads fine when I look at it today.

    What's your definition of a region?
    A non empty,connected,open set
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    (Original post by mathz)
    A non empty,connected,open set
    Then neither B, nor the boundary of B is a region.
 
 
 
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