中文摘要：

引入广义局部理想子集系统、Z-局部半连续格和强Z-局部连续格的概念,讨论了它们的基本性质,并给出了Z-局部半连续格的若干内部刻画.此外,探讨了Z-局部半连续映射与Z-局部半连续格上的函数空间,推广了相关文献的结论.

英文摘要：

The concepts of generalized locally ideal sub-systems, Z-locally semicontinuous lattices and strongly Z-locally continuous lattices are introduced and examined. Some intrinsic characterizations of Z-locally semicontinuous lattices are obtained. In addition, some properties of Z-locally semicontinuous mappings and the function space on Z-locally semicon- tinuous lattices are discussed, and the conclusions of related articles are expanded.