Metrization and Paracompact Spaces
In this chapter, we are mainly concerned with metrization and paracompact spaces. We also derive some properties of the products of compact spaces and perfect maps. Several metrization theorems are proved, and we characterize completely metrizable spaces. We will study several different characteristics of paracompact spaces that indicate, in many situations, the advantages of paracompactness. In particular, there exists a useful theorem showing that, if a paracompact space has a certain property locally, then it has the same property globally. Furthermore, paracompact spaces have partitions of unity, which is also a very useful property.
KeywordsOpen Cover Direct Limit Metrizable Space Limitation Topology Bibliographic Note
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