On fundamental groups of quotient spaces (Q649836)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On fundamental groups of quotient spaces |
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On fundamental groups of quotient spaces (English)
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6 December 2011
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The authors prove the following simple result. Let \(f:(X,x_0)\to (Y,y_0)\) be a quotient map of topological spaces, where \(X\) is locally path-connected and \(Y\) semilocally simply-connected. If each fiber \(f^{-1}(y)\) is connected, then the induced homomorphism \(f_\#:\pi_1(X,x_0)\to\pi_1(Y,y_0)\) is surjective. They illustrate this result with a series of examples.
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quotient maps
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fundamental group
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