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Question

# Let R be the unit disk $\left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 1 \right\}$ with (0, 0) removed. Is (0, 0) a boundary point of R? Is R open or closed?

Solution

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See Definition: Interior and Boundary Points

Every disk centered at (0,0) contains points in R an points not in R (the center itself), so (0,0) is a boundary point.

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