Question

1 OL . 2.9. In R2 with the standard topology, prove that Cl(a, b) x (c,d)) = [a, b] and Int([a, b] x [c, d]) = (a, b) x (c,d).

I haven't learned limit points yet so please answer it another way.

Answer 1

Solution: We have to prove that CI ((@16)x(c,d)) = [016] *[cid] in standard topology in 1R² I (ab xCcd) оа нь Clearly tor ang point on the boundary too each open set C Circular dise) containing that contain inbini tely many points of cab) XC.d) let cary) & Caib)xCc,d) either r¢lain).y & Co,d) or RE (aib), y & Cod) or 㢠caib), y e(aa). For each case from sight figure it is clearly that j atleast one Circular dise conta aining Cary) saya st. CS Scanned with Campanjer

focaib)x(Cd))= 4, -> out side point not limit point of (ab)x(cd) In other words. ci [ca,b) *C;d)) = [[c1b)*(0, d)] o [21b)Xia) = [216] « [ca] Scanned with CamScanner