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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6520 • Algebraic Topology

Summer 2023 • Question 1

Question

Math 6520 • Algebraic Topology Summer 2023 • Question 1

Prove that if \(X\) and \(Y\) are path connected spaces then

\[ \pi _1(X\times Y,(x_0,y_0))\cong \pi _1(X,x_0)\times \pi _1(Y,y_0). \]

Raw LaTeX

Prove that if \(X\) and \(Y\) are path connected spaces then

\[
\pi_1(X\times Y,(x_0,y_0))\cong \pi_1(X,x_0)\times\pi_1(Y,y_0).
\]

Topic Tags

Fundamental Groups Homotopy Groups