If $Y$ and $Z$ are connected, is $Y \times Z$ path connected? I cannot find a counter example. Some help please.
2026-03-30 23:55:38.1774914938
Product of Connected Spaces (2)
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If $Y$ and $Z$ are path connected, so is $Y\times Z$. Just take the product of paths. If $Y$ is not path connected then $Y\times Z$ cannot be path connected, otherwise the projection of a path in $Y\times Z$ would be a path in $Y$.