汕头大学学报（自然科学版）

以Diffeological向量空间赋予D拓扑为背景，杨忠强和胡泽英定义了拟拓扑向量空间，即在向量空间上赋予一个拓扑使得加法运算是分离变量连续的，同时数乘运算是连续的.本文在此基础上研究了拟拓扑向量空间的子空间、乘积空间和商空间，并给出了拟拓扑向量空间范畴的定义，进一步证明了该范畴的双完备性.

On the background of diffeological vector spaces endowed with D-topology, YANG Zhongqiang and HU Zeying defined quasi-topological vector spaces, which is a vector space with a topology satisfying the conditions that the vector addition is separately continuous and the scalar multiplication is continuous. The subspaces, product spaces, and quotient spaces of quasi-topological vector spaces are studied in this paper and the definition of the category of quasi-topological vector spaces is given. Moreover, it is proved that this category is bicomplete.