Paracompactness and Metrizability

Tej Bahadur Singh ()
Additional contact information
Tej Bahadur Singh: University of Delhi, Department of Mathematics

Chapter Chapter 9 in Introduction to Topology, 2019, pp 205-218 from Springer

Abstract: Abstract Paracompact Hausdorff spaces are very close to metrizable spaces, and have proved quite useful in differential geometry and topology. Section 9.1 concerns with the study of these spaces. It will be seen that every metric space is paracompact Hausdorff. On the other hand, a locally metrizable paracompact Hausdorff space is metrizable. In fact, there are several theorems that guarantee the metrizability of a topological space X. In the previous chapter, we have seen such a theorem, viz., the Urysohn Metrization Theorem. In Sect. 9.2, we treat the most important one, it gives a complete characterization of metric spaces.

Date: 2019
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-6954-4_9

Ordering information: This item can be ordered from
http://www.springer.com/9789811369544

DOI: 10.1007/978-981-13-6954-4_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().