Abstract
This chapter discusses the theories of paracompact spaces. The concept of paracompactness was invented by J. Dieudonne and the fundamental theorem by A. H. Stone. The paracompact spaces contain two important classical categories: compact spaces and metric spaces. A regular space R is paracompact if every open covering of R has a locally finite refinement. A T1-space R is paracompact if open covering of R has a cushioned refinement. A topological space R is called countably paracompact if every countable open covering of R has a locally finite open refinement. Every paracompact space is countably paracompact, but the converse is not true. There are various modifications of the concept of paracompactness or of full-normality though probably not so many as for the concept of compactness. The chapter discusses two modifications that are are strong paracompactness and collection-wise normality. One of them is a little stronger than paracompactness and the other a little weaker than full normality.
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