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Keywords:
countable compactness; ${M\kern -1.8pt A\kern 0.2pt }_{countable}$; topological groups; finite powers
countable compactness; ${M\kern -1.8pt A\kern 0.2pt }_{countable}$; topological groups; finite powers
Summary:
We will show that under ${M\kern -1.8pt A\kern 0.2pt }_{countable}$ for each $k \in \Bbb N$ there exists a group whose $k$-th power is countably compact but whose $2^k$-th power is not countably compact. In particular, for each $k \in \Bbb N$ there exists $l \in [k,2^k)$ and a group whose $l$-th power is countably compact but the $l+1$-st power is not countably compact.
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