International Journal of Mathematics Trends and Technology
Volume 13 | Number 1 | Year 2014 | Article Id. IJMTT-V13P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V13P502
In this paper, we gave a new topological concept and we called it The closed limit point compactness. This concept is stronger than the concept of a limit point compactness, that is, every a closed limit point compact space is a limit point compact space but the converse is not true. We have proved that the property of being a closed limit point compact is a topological property but not a hereditary property but it inherits to the closed subspace. We have shown that the continuous image of a closed limit point compact need not be a closed limit point compact. Also, we have shown that the quotient space of a closed limit point compact need not be a closed limit point compact. Finally, we have shown that if X×Y is a closed limit point compact and Y is a T1-space, then X is a closed limit point compact.
[1] Munkres J. R, “Topology”, Person Prentice Hall, Second Edition, 2009.
[2] Adams C., and Franzosa R., “ Introduction to Topology Pure and Applied”, Person Printice Hall, 2008.
[3] Morris S. A. , “Topology Without Tears”, Springer, New York, 2007.
[4] Raman M., “A pedagogical history of compactness”, arXiv: 1006.4131v1 , [math.HO] 21 Jun 22, 2010.
[5] Sharma J.N.,”Topology”, Manoj Printers, 1977.
Abedal-Hamza Mahdi Hamza, Saba N. Faisel Al-khafaji, Aqeel K. Al-khafaji, "The Closed Limit Point Compactness," International Journal of Mathematics Trends and Technology (IJMTT), vol. 13, no. 1, pp. 10-12, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V13P502
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