Normal Topological Spaces
Normal Topological Spaces
复制标题
正规拓扑空间
DOI：
--
复制
发表时间：
1974
期刊：
影响因子：
--
通讯作者：
H. Shapiro
中科院分区：
文献类型：
--
作者：
R. Aló;H. Shapiro
本文桥梁的差距存在于集理论拓扑领域之间的介绍性文本和更专业的专著。作者回顾了一般拓扑学的发展，并讨论了重要的新研究领域和定义一种适用于这一活跃数学领域的方法的重要性。详细考虑了正规覆盖的概念和相关思想，以及正规空间的特征，集合正规空间及其与准紧空间（以及其他较弱的紧性形式）的相互关系。在考虑m空间等新概念及其与已有概念的关系之前，研究了嵌入子空间的各种方法。这些思想被应用于给出关于连续向量值函数扩展的新结果。我们还研究了Wallman Frink紧化和real紧化，通过使用更一般的l -滤波器来帮助统一思想。
This text bridges the gap existing in the field of set theoretical topology between the introductory texts and the more specialised monographs. The authors review fit developments in general topology and discuss important new areas of research and the importance of defining a methodology applicable to this active field of mathematics. The concept of normal cover and related ideas is considered in detail, as are the characterisations of normal spaces, collectionwise normal spaces and their interrelationships with paracompact spaces (and other weaker forms of compactness). Various methods of embedding subspaces are studied, before considering newer concepts such as M-spaces and their relationships with established ideas. These ideas are applied to give new results pertaining to the extension of continuous vector-valued functions. Wallman Frink compactifications and realcompactifications are also studied to assist in unifying the ideas through the use of the more general L-filter."