Given a $T_0$ paratopological group G and a class $\mathcal{C}$ of continuous homomorphisms of paratopological groups, we define the $\mathcal{C}$-semicompletion $\mathcal{C}[G)$ and $\mathcal{C}$-completion $\mathcal{C}[G]$ of the group G that contain G as a dense subgroup, satisfy the $T_0$-separation axiom and have certain universality properties. For special classes $\mathcal{C}$, we present some necessary and sufficient conditions on G in order that the (semi)completions $\mathcal{C}[G)$ and $\mathcal{C}[G]$ be Hausdorff. Also, we give an example of a Hausdorff paratopological abelian group G whose $\mathcal{C}$-semicompletion $\mathcal{C}[G)$ fails to be a $T_1$-space, where $\mathcal{C}$ is the class of continuous homomorphisms of sequentially compact topological groups to paratopological groups. In particular, the group G contains an ω-bounded sequentially compact subgroup H such that H is a topological group but its closure in G fails to be a subgroup.

给定一个 ${吨}_0$超拓扑群G和一个类$\mathcal{C}$ 的互补拓扑群的连续同态，我们定义 $\mathcal{C}$-半完成 $\mathcal{C}[G)$ 和 $\mathcal{C}$-完成 $\mathcal{C}[G]$该组的ģ包含ģ作为致密子群，满足${吨}_0$-分离公理并具有一定的普适性。对于特殊班$\mathcal{C}$，我们提出G上的一些充要条件，以便（半）完成$\mathcal{C}[G)$ 和 $\mathcal{C}[G]$成为豪斯多夫。此外，我们还给出了一个 Hausdorff 副拓扑阿贝尔群G的例子，它的$\mathcal{C}$-半完成 $\mathcal{C}[G)$ 不是一个 ${吨}_1$-空间，哪里 $\mathcal{C}$是顺序紧拓扑群到副拓扑群的连续同态类。特别地，群G包含一个ω 有界的顺序紧致子群H，使得H是一个拓扑群，但它在G 中的闭包不能是一个子群。