Let $I=[0,1]$, $A=\{0\}\cup\{\frac{1}{n}\}_{n\ge 1}$. Prove that there is no retraction from $I\times I$ to $I\times \{0\}\cup A\times I$.
Let $X$ be path-connected and $Y$ be arbitrary topological space. Then the join $X*Y$ is simply connected. $\textbf{Proof}.$ We use Van K...
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