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universal algebra; paratopological group; topological group
Let $(L,\Cal T)$ be a Tychonoff (regular) paratopological group or algebra over a field or ring $K$ or a topological semigroup. If $\operatorname{nw}(L,\Cal T)\leq \tau$ and $\operatorname{nw}(K)\leq\tau $, then there exists a Tychonoff (regular) topology $\Cal T^*\subseteq \Cal T$ such that $w(L,\Cal T^*)\leq\tau$ and $(L,\Cal T^*)$ is a paratopological group, algebra over $K$ or a topological semigroup respectively.
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