Consider the topological space $\mathbb{R}$ and the subset $\mathbb{Q}$ which has as many components as elements and is therefore totally unconnected. Now consider the product space $\mathbb{Q}\times\mathbb{Q}$. How many components does the product space have? I would assume it's |$\mathbb{Q}$|^2, because we have |$\mathbb{Q}$|^2 elements which are totally unconnected. I'm not quite sure if I got it right, and do understand how the number of components translates into the product space in general. Help is appreciated.
2026-03-28 10:27:19.1774693639
Number of components of topological space
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