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Pedro Perez
Pedro Perez
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Suppose $X$ is a metric space and $A$ is a subspace of $X$ homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ from $X$ onto $A$ such that $r^{-1}(v)=\{v\}$? Thanks

Suppose $X$ is a metric space and $A$ is a subspace homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ from $X$ onto $A$ such that $r^{-1}(v)=\{v\}$? Thanks

Suppose $X$ is a metric space and $A$ is a subspace of $X$ homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ from $X$ onto $A$ such that $r^{-1}(v)=\{v\}$? Thanks

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Pedro Perez
Pedro Perez
  • 33
  • 3

Special retraction from a metric space onto an arc

Suppose $X$ is a metric space and $A$ is a subspace homeomorphic to $[0,1]$ with its usual topology. Let $v$ an end point of $A$, that is $v$ does not disconnect $A$. Is there a retraction $r$ from $X$ onto $A$ such that $r^{-1}(v)=\{v\}$? Thanks