We study the Raĭkov completion $\check{G}$ of a paratopological group G defined by Banakh-Ravsky in 2020. This permits to Banakh and Tkachenko introduce the notion of $\mathcal{C}$-semicompletion, where $\mathcal{C}$ is a class of continuous homomorphisms of paratopological groups. We show that the product of $\mathcal{C}$-semicompletions is a $\mathcal{C}$-semicompletion for the product of arbitrary paratopological groups. In particular, if we consider the class $\mathcal{C}$ of all continuous homomorphisms between paratopological groups, we obtain that $\check{G}={\prod }_{i\in I}{\check{G}}_i$. We also study the interaction between $\mathcal{C}$-semicompletions of a paratopological group G and the $\mathcal{C}$-semicompletions of subgroups of G.

We prove that if G is a $T_3$ paratopological group, then every $\mathcal{C}$-semicompletion of G is $T_3$. We show that if G is first-countable (second-countable), then every $\mathcal{C}$-semicompletion of G is first-countable (second-countable). Therefore, if G is metrizable separable, then every $\mathcal{C}$-semicompletion of G is metrizable separable as well.

我们研究 Raĭkov 完成 $\check{G}$由 Banakh-Ravsky 在 2020 年定义的超拓扑群G。这允许 Banakh 和 Tkachenko 引入概念$\mathcal{C}$-半完成，其中$\mathcal{C}$是一类互补拓扑群的连续同态。我们证明了产品$\mathcal{C}$-半完成是一个 $\mathcal{C}$- 任意副拓扑群的产物的半完成。特别地，如果我们考虑类$\mathcal{C}$ 对所有互补拓扑群之间的连续同态，我们得到 $\check{G}={\prod }_{\mathrm{一世}\in \mathrm{一世}}{\check{G}}_{\mathrm{一世}}$. 我们还研究了$\mathcal{C}$- 一个超拓扑群G和$\mathcal{C}$- G的子群的半完成。

我们证明如果G是一个${吨}_3$ 超拓扑群，那么每个 $\mathcal{C}$的-semicompletion ģ是${吨}_3$. 我们证明如果G是第一可数（第二可数），那么每个$\mathcal{C}$的-semicompletion ģ是第一可数（第二可数）。因此，如果G是可度量可分的，那么每$\mathcal{C}$的-semicompletion ģ是度量化可分离为好。