Give an example of a bounded domain and a piecewise $C^1$ closed curve satisfy given conditions.
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Give an example of a bounded domain $Omega subset mathbb {C}$ and a piecewise $C^1$ closed curve $f$ in $Omega$ such that $I(f;z)=5$ for some $z in mathbb {C}/Omega$. (Here $C^1$ means the components have continuous derivatives for all t within the interval $[a,b]$. And $I(f;z)=5$ is the winding number of $f$ on $z$.)
Give an example of a bounded domain $Omega subset mathbb {C}$ and a cycle $Gamma=rho_1 + rho_2 + dots +rho_s$ for some $sin mathbb {Z}_+$, such that
- each $rho_i$ is a $C^1$ simple closed cuve in $Omega$,
- no two $rho_i, rho_j$ intersect, and
- for every $k in {1, dots,5}$ there is a point $a_kin {C}/Omega$ such that $I(Gamma;a_k)=k$.
complex-analysis winding-number
asked Nov 18 at 18:16
wtnmath
15212
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Give an example of a bounded domain $Omega subset mathbb {C}$ and a piecewise $C^1$ closed curve $f$ in $Omega$ such that $I(f;z)=5$ for some $z in mathbb {C}/Omega$. (Here $C^1$ means the components have continuous derivatives for all t within the interval $[a,b]$. And $I(f;z)=5$ is the winding number of $f$ on $z$.)
Give an example of a bounded domain $Omega subset mathbb {C}$ and a cycle $Gamma=rho_1 + rho_2 + dots +rho_s$ for some $sin mathbb {Z}_+$, such that
- each $rho_i$ is a $C^1$ simple closed cuve in $Omega$,
- no two $rho_i, rho_j$ intersect, and
- for every $k in {1, dots,5}$ there is a point $a_kin {C}/Omega$ such that $I(Gamma;a_k)=k$.
complex-analysis winding-number
asked Nov 18 at 18:16
wtnmath
15212
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Give an example of a bounded domain $Omega subset mathbb {C}$ and a piecewise $C^1$ closed curve $f$ in $Omega$ such that $I(f;z)=5$ for some $z in mathbb {C}/Omega$. (Here $C^1$ means the components have continuous derivatives for all t within the interval $[a,b]$. And $I(f;z)=5$ is the winding number of $f$ on $z$.)
Give an example of a bounded domain $Omega subset mathbb {C}$ and a cycle $Gamma=rho_1 + rho_2 + dots +rho_s$ for some $sin mathbb {Z}_+$, such that
- each $rho_i$ is a $C^1$ simple closed cuve in $Omega$,
- no two $rho_i, rho_j$ intersect, and
- for every $k in {1, dots,5}$ there is a point $a_kin {C}/Omega$ such that $I(Gamma;a_k)=k$.
complex-analysis winding-number
asked Nov 18 at 18:16
wtnmath
15212
Give an example of a bounded domain $Omega subset mathbb {C}$ and a piecewise $C^1$ closed curve $f$ in $Omega$ such that $I(f;z)=5$ for some $z in mathbb {C}/Omega$. (Here $C^1$ means the components have continuous derivatives for all t within the interval $[a,b]$. And $I(f;z)=5$ is the winding number of $f$ on $z$.)
Give an example of a bounded domain $Omega subset mathbb {C}$ and a cycle $Gamma=rho_1 + rho_2 + dots +rho_s$ for some $sin mathbb {Z}_+$, such that
- each $rho_i$ is a $C^1$ simple closed cuve in $Omega$,
- no two $rho_i, rho_j$ intersect, and
- for every $k in {1, dots,5}$ there is a point $a_kin {C}/Omega$ such that $I(Gamma;a_k)=k$.
complex-analysis winding-number
complex-analysis winding-number
asked Nov 18 at 18:16
wtnmath
15212
asked Nov 18 at 18:16
wtnmath
15212
asked Nov 18 at 18:16
wtnmath
15212
asked Nov 18 at 18:16
wtnmath
15212
asked Nov 18 at 18:16
wtnmath
15212
15212
add a comment |
add a comment |
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