Houston Problem Book Problem 27

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Problem 27 (HPB): Suppose $M$ is an $n$-dimensional compact metric space and $A$ is the set of all unstable points of $M$. Does there exist a homotopy $f(\cdot,t)$ of $M$ to $M$ such that $f(\cdot,0)$ is the identity and $f(M,t)$ and $A$ do not intersect for each $t>0$? (Asked by W. Kuperberg, 13 September 1972)

Answer: No (W. Kuperberg and P. Minc, 28 March 1979)