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Post Closed as "Needs more focus" by abx, Igor Belegradek, YCor, Noah Schweber, Yemon Choi
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THC
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Is there a way to see whether a topological space $\Omega$ does not allow retractions $r: \Omega \mapsto B$, with $B$ an arbitrarya given subspace of $\Omega$ ?

In other words: when is a space not retractable to a given subspace $B$ ?

Is there a way to see whether a topological space $\Omega$ does not allow retractions $r: \Omega \mapsto B$, with $B$ an arbitrary subspace of $\Omega$ ?

In other words: when is a space not retractable ?

Is there a way to see whether a topological space $\Omega$ does not allow retractions $r: \Omega \mapsto B$, with $B$ a given subspace of $\Omega$ ?

In other words: when is a space not retractable to a given subspace $B$ ?

Source Link
THC
  • 4.5k
  • 21
  • 33

Topological spaces without retracts

Is there a way to see whether a topological space $\Omega$ does not allow retractions $r: \Omega \mapsto B$, with $B$ an arbitrary subspace of $\Omega$ ?

In other words: when is a space not retractable ?