About The Line In Star Domain

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Definition from wikipedia :




In mathematics, a set $S$ in the Euclidean space $mathbbR^n$ is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an $x_0$ in $S$ such that for all $x$ in $S$ the line segment from $x_0$ to $x$ is in $S$




What are the requirements on the line segment? it must be a straight line? right? if no, so every simple-connected set will be a star domain which is incorrect




general-topology




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    yes a straight line, so that for all $xin S$ we have $x_0+t(x-x_0):tin[0,1]subseteq S$.
    – Pink Panther
    Jul 29 at 14:23














up vote
0
down vote

favorite












Definition from wikipedia :




In mathematics, a set $S$ in the Euclidean space $mathbbR^n$ is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an $x_0$ in $S$ such that for all $x$ in $S$ the line segment from $x_0$ to $x$ is in $S$




What are the requirements on the line segment? it must be a straight line? right? if no, so every simple-connected set will be a star domain which is incorrect




general-topology




share|cite|improve this question

















  • 1




    yes a straight line, so that for all $xin S$ we have $x_0+t(x-x_0):tin[0,1]subseteq S$.
    – Pink Panther
    Jul 29 at 14:23












up vote
0
down vote

favorite









up vote
0
down vote

favorite











Definition from wikipedia :




In mathematics, a set $S$ in the Euclidean space $mathbbR^n$ is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an $x_0$ in $S$ such that for all $x$ in $S$ the line segment from $x_0$ to $x$ is in $S$




What are the requirements on the line segment? it must be a straight line? right? if no, so every simple-connected set will be a star domain which is incorrect




general-topology




share|cite|improve this question













Definition from wikipedia :




In mathematics, a set $S$ in the Euclidean space $mathbbR^n$ is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an $x_0$ in $S$ such that for all $x$ in $S$ the line segment from $x_0$ to $x$ is in $S$




What are the requirements on the line segment? it must be a straight line? right? if no, so every simple-connected set will be a star domain which is incorrect





general-topology





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edited Jul 29 at 14:48









Bernard

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110k635102









asked Jul 29 at 14:19









newhere

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  • 1




    yes a straight line, so that for all $xin S$ we have $x_0+t(x-x_0):tin[0,1]subseteq S$.
    – Pink Panther
    Jul 29 at 14:23












  • 1




    yes a straight line, so that for all $xin S$ we have $x_0+t(x-x_0):tin[0,1]subseteq S$.
    – Pink Panther
    Jul 29 at 14:23







1




1




yes a straight line, so that for all $xin S$ we have $x_0+t(x-x_0):tin[0,1]subseteq S$.
– Pink Panther
Jul 29 at 14:23




yes a straight line, so that for all $xin S$ we have $x_0+t(x-x_0):tin[0,1]subseteq S$.
– Pink Panther
Jul 29 at 14:23










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Yes, the phrase "line segment" means a straight line.






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    Yes, the phrase "line segment" means a straight line.






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      Yes, the phrase "line segment" means a straight line.






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        Yes, the phrase "line segment" means a straight line.






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        Yes, the phrase "line segment" means a straight line.







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        answered Jul 29 at 14:22









        Daniel Mroz

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