Prove that an open ball in R2 is connectedSolutiona i am thi

Prove that an open ball in R2 is connected.

Solution

a) i am thinking open ball it\'s imagen like a circle

   and if we take as below way,

here we can clearly observe r1,r2 are conected.

if you consider path gx+fy+c, the ball here circle will satisfy it.

i,e

x^2+y^2+2gx+2fy+c=0

From that we can say r is connected.