A REMARK ON HEINE-BOREL THEOREM

S. Khorshidvandpour

Abstract


In the short study, we present a contradiction which comes from ignoring a hidden assumption in Heine-Borel theorem. Finally, we prove a useful theorem which rectifies the contradiction.

2010 Mathematics subject Classification: 30L99

Keywords and Phrases: Metric Space, Compactness, Heine-Borel Theorem


References


W. Rudin, “Principles of Mathematical Analysis” , 3rd Ed, McGraw-Hill,New York,1976.

R. Williamson and L. Janos, Constructing Metrics With The Heine-Borel Property, Proceedings of American Mathematical Society,100(3), 1987.

E. Kreyszig, “Introductory Functional Analysis with applications”, 1st Ed, John Wiley and Sons, Canada, 1987.

S. Willard, “General Topology” , Addison-Wesley, Reading, Ma, 1970.


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