$f(z) = z^3$ then $f(B(x,delta)) = B(y,epsilon)$?
$begingroup$
Let $f:mathbb{C}rightarrow mathbb{C}$ such that $f(z) = z^3$
Let $xinmathbb{C}$ and $delta > 0$
Is true that $f(B(x,delta)) = B(y,epsilon)$ for some $yin mathbb{C}$ and some $epsilon > 0$ ?
Where $B(x,delta) = $ { $ainmathbb{C} : |a-x|<delta$ }
general-topology complex-analysis
edited Jan 9 at 4:20
Robert Lewis
47k23067
asked Jan 9 at 2:45
ZAFZAF
4357
$endgroup$
add a comment |
$begingroup$
Let $f:mathbb{C}rightarrow mathbb{C}$ such that $f(z) = z^3$
Let $xinmathbb{C}$ and $delta > 0$
Is true that $f(B(x,delta)) = B(y,epsilon)$ for some $yin mathbb{C}$ and some $epsilon > 0$ ?
Where $B(x,delta) = $ { $ainmathbb{C} : |a-x|<delta$ }
general-topology complex-analysis
edited Jan 9 at 4:20
Robert Lewis
47k23067
asked Jan 9 at 2:45
ZAFZAF
4357
$endgroup$
3
$begingroup$
Not in general. An exception is the case $x=0$.
$endgroup$
– Sangchul Lee
Jan 9 at 2:54
add a comment |
$begingroup$
Let $f:mathbb{C}rightarrow mathbb{C}$ such that $f(z) = z^3$
Let $xinmathbb{C}$ and $delta > 0$
Is true that $f(B(x,delta)) = B(y,epsilon)$ for some $yin mathbb{C}$ and some $epsilon > 0$ ?
Where $B(x,delta) = $ { $ainmathbb{C} : |a-x|<delta$ }
general-topology complex-analysis
edited Jan 9 at 4:20
Robert Lewis
47k23067
asked Jan 9 at 2:45
ZAFZAF
4357
$endgroup$
Let $f:mathbb{C}rightarrow mathbb{C}$ such that $f(z) = z^3$
Let $xinmathbb{C}$ and $delta > 0$
Is true that $f(B(x,delta)) = B(y,epsilon)$ for some $yin mathbb{C}$ and some $epsilon > 0$ ?
Where $B(x,delta) = $ { $ainmathbb{C} : |a-x|<delta$ }
general-topology complex-analysis
general-topology complex-analysis
edited Jan 9 at 4:20
Robert Lewis
47k23067
asked Jan 9 at 2:45
ZAFZAF
4357
edited Jan 9 at 4:20
Robert Lewis
47k23067
asked Jan 9 at 2:45
ZAFZAF
4357
edited Jan 9 at 4:20
Robert Lewis
47k23067
edited Jan 9 at 4:20
Robert Lewis
47k23067
edited Jan 9 at 4:20
Robert Lewis
47k23067
47k23067
asked Jan 9 at 2:45
ZAFZAF
4357
asked Jan 9 at 2:45
ZAFZAF
4357
asked Jan 9 at 2:45
ZAFZAF
4357
4357
3
$begingroup$
Not in general. An exception is the case $x=0$.
$endgroup$
– Sangchul Lee
Jan 9 at 2:54
add a comment |
3
$begingroup$
Not in general. An exception is the case $x=0$.
$endgroup$
– Sangchul Lee
Jan 9 at 2:54
3
3
$begingroup$
Not in general. An exception is the case $x=0$.
$endgroup$
– Sangchul Lee
Jan 9 at 2:54
$begingroup$
Not in general. An exception is the case $x=0$.
$endgroup$
– Sangchul Lee
Jan 9 at 2:54
add a comment |
0
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3
$begingroup$
Not in general. An exception is the case $x=0$.
$endgroup$
– Sangchul Lee
Jan 9 at 2:54