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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2017 • Question 7

Question

Math 6510 • Differentiable Manifolds Fall 2017 • Question 7

Prove that if \(X\) and \(Y\) are path connected spaces, then \(\pi _1(X\times Y)=\pi _1(X)\times \pi _1(Y)\).

Raw LaTeX

Prove that if \(X\) and \(Y\) are path connected spaces, then
\(\pi_1(X\times Y)=\pi_1(X)\times\pi_1(Y)\).

Topic Tags

Fundamental Groups Homotopy Groups