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Math · Advanced Math
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Please answer all questions a) to e)
(1) For each subset of R2 below, draw a picture of the subset using the usual conventions (dotted lines for boundaries not included in the subset, open circles for points on the boundary of the subset but not in it, closed circles, solid lines, and shaded regions to indicate points in the subset). Then deter- mine whether the subset is not open, open but not a domain (i.e. open but not connected), or a domain. If the subset is not open, given a point P in the subset such that no disk around P is contained in the subset. If the subset is open but not a domain, express it as a union UUV of two non-empty open subsets U, V with Un V = 0. (b) {(x,y) : xy 1) (d) (x, y)a>y>0 and < 5) (e){(x, y) : 0 < x and 0 < y x}
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