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$AcapLambda$ polynomially convex in $Lambda$

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0

$begingroup$

Let $ASubsetBbb C^n$ polynomially convex, that is its convex hull
$$
widehat A:=zinBbb C^n;:;
$$
coincides with $A$.

Consider then $LambdasubsetBbb C^n$ such that $LambdasimeqBbb C$ (say, for example $Lambda=Bbb Ce_1$, where $e_1=(1,0,dots)inBbb C^n$).

How can I prove that $AcapLambda$ is polynomially convex in $Lambda$? How can one deduce from this that $Lambdasetminus A$ is connected?

EDIT: Could this a particular case of the following statemen?

$A,BSubsetBbb C^n$ polynomially convex $Rightarrow$ $Acup B$ p.c.

general-topology complex-analysis several-complex-variables

share|cite|improve this question

edited Mar 23 at 11:24

Joe

asked Mar 21 at 14:24

JoeJoe

7,23921229

$endgroup$

add a comment | 

0

$begingroup$

Let $ASubsetBbb C^n$ polynomially convex, that is its convex hull
$$
widehat A:=zinBbb C^n;:;
$$
coincides with $A$.

Consider then $LambdasubsetBbb C^n$ such that $LambdasimeqBbb C$ (say, for example $Lambda=Bbb Ce_1$, where $e_1=(1,0,dots)inBbb C^n$).

How can I prove that $AcapLambda$ is polynomially convex in $Lambda$? How can one deduce from this that $Lambdasetminus A$ is connected?

EDIT: Could this a particular case of the following statemen?

$A,BSubsetBbb C^n$ polynomially convex $Rightarrow$ $Acup B$ p.c.

general-topology complex-analysis several-complex-variables

share|cite|improve this question

edited Mar 23 at 11:24

Joe

asked Mar 21 at 14:24

JoeJoe

7,23921229

$endgroup$

add a comment | 

$begingroup$

Let $ASubsetBbb C^n$ polynomially convex, that is its convex hull
$$
widehat A:=zinBbb C^n;:;
$$
coincides with $A$.

Consider then $LambdasubsetBbb C^n$ such that $LambdasimeqBbb C$ (say, for example $Lambda=Bbb Ce_1$, where $e_1=(1,0,dots)inBbb C^n$).

How can I prove that $AcapLambda$ is polynomially convex in $Lambda$? How can one deduce from this that $Lambdasetminus A$ is connected?

EDIT: Could this a particular case of the following statemen?

$A,BSubsetBbb C^n$ polynomially convex $Rightarrow$ $Acup B$ p.c.

general-topology complex-analysis several-complex-variables

share|cite|improve this question

edited Mar 23 at 11:24

Joe

asked Mar 21 at 14:24

JoeJoe

7,23921229

$endgroup$

share|cite|improve this question

edited Mar 23 at 11:24

Joe

asked Mar 21 at 14:24

JoeJoe

7,23921229

share|cite|improve this question

edited Mar 23 at 11:24

Joe

asked Mar 21 at 14:24

JoeJoe

7,23921229

asked Mar 21 at 14:24

JoeJoe

7,23921229

asked Mar 21 at 14:24

JoeJoe

7,23921229