基-中紧映射性质和基-可数中紧乘积性质

Property of Base-mesocompact mapping and base-countable mesocompact product

引入了基-中紧映射,并证明了如下结果:①设f:X→Y是闭Lindelff映射,若X为正则空间,则f:X→Y是基-中紧映射;②若X和Y都为基-可数中紧的,Y为局部紧的,则X×Y为基-可数中紧的.

The notion of base-mesocompact mapping is introduced and the following results are proved：（1）Let f：X--＋Y be a closed Lindeloff mapping. If X is regular, then f：X→Y is base-countable mesocompact mapping; （2） Let X and Y be both base-mesocompact. X x Y is base-countable mesocompact if Y is locally compact.