Question

Find the interior, closure, and boundary of:

aQCR b)R CRP c) A = {(2,y) y >0} CR?

Answer 1

SIA @ QER. Let BEQ. Then any interval (a,b) containing will contain irrational point (By density property of @). =) int(Q) = 0 By density 2 - R. a Bomdomy of a » Bondermy of ) A a an he [a. Ria] & ROR=R D © ORSR Let Mo) E R CR² Then any ball B (9, 2) = R² which contarins (0,0) will contain points (M, Y,) s to y zo =) Bp (Y,Z) & R. » mt (R) - $ det, (2010) (9,2) 9) Ungd 200. a) (4,2) » (3,0) ER Ř - R SR² Bd (IR) - Řn CR? (R) o RA1R² =R

WASOMALE © As {ay) : y20} <R? ( Let (ny) EASR2 sit. y po consider the ball By (ny) - ball centersed at (ny) of padius . then cleanly By (my) ea f it contains x y) Now any ball containing (0,0) E A will intersect lowers half plane. - int (A) = {(ny): y los if an, Y) E A pit (m, n) (x,y) " an 4 by since » " %30 ,V na 1 y zo N,Y) EA. Bd (A) - Ā A CR²A) - AMR = {no): NER}.