Consider a neighborhood Dr (p) CR" (defined with the standard Euclidean norm ||- ||2) of radius r > 0 with center pER".

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Consider A Neighborhood Dr P Cr Defined With The Standard Euclidean Norm 2 Of Radius R 0 With Center Per 1 (28.79 KiB) Viewed 11 times

Consider a neighborhood Dr (p) CR" (defined with the standard Euclidean norm ||- ||2) of radius r > 0 with center pER". A deleted neighborhood is a set of the form Nr. (p) = { Dr (p): z p}. That is, N, (p) is a neighborhood of radius r> 0 with its center point p removed. Assuming that p = 0: (a) Show that the center p= 0 belongs to ON,(0) (the boundary of N, (0)). (b) Sketch the complement (N,(0)) and clearly indicate the boundary.