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Apr 2, 2021 at 13:32 comment added Vladimir47 Great answer! Thank you.
Apr 2, 2021 at 6:04 history edited YCor
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Apr 2, 2021 at 6:04 comment added YCor Both are false even in the additive group $\mathbf{C}^2$. Take $X$ the hyperbola $\{(x,y):xy=1\}$ and $Y$ the closed subgroup $\{(x,y):y=0\}$. Then $X+Y=\{(x,y):y\neq 0\}$ is not closed.
Apr 2, 2021 at 5:55 history edited YCor CC BY-SA 4.0
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Apr 2, 2021 at 5:48 history asked Vladimir47 CC BY-SA 4.0