中文摘要：

本文主要刻画第一可数拟拓扑群乘积空间的子群,得如下结论：1）设G是满足T_1分离公理的拟拓扑群,则G拓扑同构于一族满足第一可数且满足T_1分离公理拟拓扑群乘积空间的子群当且仅当G是w-balanced和局部w-good;2）设G是满足T_2分离公理的拟拓扑群,则G拓扑同构于一族满足第一可数且满足T_2分离公理拟拓扑群乘积空间的子群当且仅当G是w-balanced、局部w-good和Hs（G）≤w;3）设G是满足正则分离公理的拟拓扑群,则G拓扑同构于一族满足第一可数且满足正则分离公理拟拓扑群乘积空间的子群当且仅当G是w-balanced、局部w-good和Ir（G）≤w.

英文摘要：

In this paper,we mainly discuss the projectively first-countable quasitopological groups.The following results are obtained： 1） Let G be a T_1 quasitopological group,then G is projectively T_1 first-countable if and only if G is w-balanced and locally w-good.2）Let G be a Hausdorff quasitopological group,then G is projectively Hausdorff first-countable if and only if G is w-balanced,locally w-good and Hs（G）≤w.3） Let G be a regular quasitopological group,then G is projectively regular first-countable if and only if G is w-balanced,locally w-good and Ir（G）≤w.