Question

topology

Consider The The for and radius 1 in see R² with felloeding secrets delay) : _ 14-442+ IV-vel doo (ny) = max { 10 -4 2/V-val} XELU, 4) and y = 1 U2 V22 a) Sketch open ball Billo centered al (1,1) both (R3 d.) and (IR² doo) prove That if u is open subset of (R², do it is also an open subset of (R² doo) @ Also -Prove that if u is open subset (R², do then it is open subset of (2) then.

Answer 1

(QS @le B(1,1) free d((w.y),(1,1)) </ 12-11 +17-11c1 (27) EB (1,1) doo (lay), (1.1)) (1 max. ax{17-11947-11}</ (0,2) F Cins an (oro) (b) This is enough to prove. B doo (n. e) C Bd Ca, d) let YE B. (a, E) da (nog) ce - (21.8+ y=(n2, 42) 121-121 + 171 721 LE max {121-82), ry, Y21} CE XE Bar (x,e) Therefore, every open set of CR, d.) ano of (IR, doo) open set

@ similarly reti Y & Bd, (5,2) 197-491 +144-Y max{121-82), (71-721} ce → 121-821 se, 17 - Y2 | CE 121-821 & 171 - 72 | Le to my & B da (2, 26) Bdi (2,6) CB doo (x, RE) every open set subset of the do) SO of (IR, doo) in CR, di)