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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

5 votes
2 answers
557 views

If $E$ maps onto a contractible space with contractible fibers, must $E$ be contractible?

Let $p\colon E\to C$ be a continuous, surjective map between topological spaces with $C$ contractible. Suppose that $p^{-1}(c)$ is contractible for each $c\in C$. Is it true that $E$ is weakly contrac …
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