Non-Compactness of a Closed and Bounded Set

Authors

  • Bishnu Prasad Dhungana Mahendra Ratna Campus, Kathmandu

DOI:

https://doi.org/10.3126/kuset.v10i1.63685

Keywords:

Compactness, Heine-Borel property, Metric space, Banach space

Abstract

If every closed and bounded set in a metric space is compact, the space is said to have the Heine-Borel property. This property holds in every finite dimensional normed space, but may not be true in general. Though its proof appears in many basic analysis courses, it is hard to motivate as the result is subtle and the applications are not obvious. Our goal is to provide an elegant proof as a resource for teachers that will enable them to motivate the study of this essential property and to understand the mathematics in it as a valuable teaching tool. 

Downloads

Download data is not yet available.
Abstract
35
PDF
24

Downloads

Published

2014-11-30

How to Cite

Dhungana, B. P. (2014). Non-Compactness of a Closed and Bounded Set. Kathmandu University Journal of Science, Engineering and Technology, 10(1), 28–31. https://doi.org/10.3126/kuset.v10i1.63685

Issue

Vol. 10 No. 1 (2014)

Section

Original Research Articles

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

This license enables reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use. If you remix, adapt, or build upon the material, you must license the modified material under identical terms.