I have been trying to solve the problem. Since the function is defined for the values taken from the three given sets, it seems that $(2)$ is one of the right options. But, I cannot determine the answer for the other options. Could someone point me in the right direction? Thanks in advance for your time.
Consider the three subsets of $\mathbb R^2$
0
$\begingroup$
real-analysis
analysis
continuity
-
1Hints: I'd suggest ignoring the continuity condition at first, and putting it back in at the end to see if it changes anything. Then draw the sets $A_1,A_2,A_3$. Do they overlap at all? Why is that relevant? – 2012-12-19
1 Answers
3
Hint: $A_1 \cap A_2 =\{ (1,0) \}$, but $A_3$ is "far away"...
This means that $A_1\cup A_2$ is connected, and $A_1 \cup A_2 \cup A_3$ is not.
-
0Thanks for the hint,sir.It means that choice $(4)$ is right,i guess. – 2012-12-19