摘要
函数的插入和扩张是一般拓扑学中的经典问题，很多重要的覆盖性质和函数插入理论存在密切的关系。近些年来，关于函数空间的刻画备受关注，本文引入上半连续集值映射的概念，使用这样的概念，我们将会回答谢和燕提出的问题。
匈牙利数学家Á.Császár在1997年提出了广义拓扑空间的概念。他是经典一般拓扑学的重要推广，广义拓扑理论近年来得到了快速发展，很多一般拓扑学的重要概念被应用于广义拓扑理论。经过十几年来的发展，广义拓扑空间的理论体系已经基本构建完毕，本文将在Á.Császár等人的基础上研究广义半层空间和函数插入的关系。
本文安排如下：
第一章 介绍了课题研究的背景知识及我们得到的主要结果内容。
第二章 上半连续集值映射的概念将会被介绍，使用这样的概念，我
们给出了和半层空间的刻画。
第三章我们引入了半层空间的概念，给出了半层空间的若干刻画，且从函数插入角度给出了该类空间刻画。
关键词：广义拓扑空间；广义函数；半层空间；集值映射；上半连续映射；空间；半层空间
The insertion and expansion of functions is a classic problem in general topology, and many important covering properties are closely related to the theory of function insertion. In recent years, the description of function space has attracted much attention. In this paper, we introduce the concept of upper semicontinuous set valued mappings, and use this concept, we will answer Xie Heyan's questions.
.Cs SZ, a Hungarian mathematician MAS, R proposed a concept of Generalized Topological Space in 1997. He is an important generalization of classical general topology. Generalized topology theory has been developing rapidly in recent years. Many important concepts of general topology are applied to generalized topology theory. After many years development, the theoretical system of generalized topological space has been basically completed construction, this paper will study the generalized semi space and function layer inserted in the.Cs SZ, MAS based on R et al.
This article is arranged as follows:
The first chapter introduces the background knowledge and the main content of the research.
In the second chapter, the concept of upper semicontinuous set - valued mapping will be introduced, using this concept, I
The portrayal of the semi - layer space is given.
In the third chapter, we introduce the concept of semi - layer space, give some characterization of the semi - layer space, and give the portrayal of this kind of space from the angle of function insertion.
Key words: Genera