Question Solved1 Answer .. 3. Let U = {(x1,x2) € R2 : 22 0}. Find all interior points of U and all boundary points of U. Is U an open set? Is U a closed set?

AFOOCU The Asker · Advanced Mathematics

Transcribed Image Text: .. 3. Let U = {(x1,x2) € R2 : 22 < x1, and Xı >0}. Find all interior points of U and all boundary points of U. Is U an open set? Is U a closed set?
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Transcribed Image Text: .. 3. Let U = {(x1,x2) € R2 : 22 < x1, and Xı >0}. Find all interior points of U and all boundary points of U. Is U an open set? Is U a closed set?
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The set&#160;&#160;is sketched below. Note that the origin does not belong to this set. &#160; The boundary points are {(x_(1),x_(2)):x_(2)=+-x_(1),x_(1) > 0} It follows directly from the definition of a boundary point. Note that any open ball&#160;centered at the above mentioned points contains points of both the sets&#160;&#160;and&#160;&#160;U^(@).&#160; The interior points are {(x_(1),x_(2)):|x_(2)| < x_(1),x_(1) > 0} This also follows directly from the definition of an interior point. Note that there exists an open ball&#160;centered at every&#160 ... See the full answer