The Open Limit Point Compactness
DOI:
https://doi.org/10.31642/JoKMC/2018/020204Keywords:
product space, , limit point, compact, limit point compact.Abstract
In this paper, we gave a new topological concept and we called it the open limit point compactness.We have proved that each of the compactness, and the limit point compactness is stronger than of the open limit point compactness., that is, compactness implies open limit point compactness, also limit point compactness implies open limit point compactness, but the converse is not true. Also we have shown that the continuous image of an open limit point compact is an open limit point compact and so this property is a topological property .This property is not a hereditary property. Connected spaces are open limit point spaces. The one-point compactification of a space is an open limit point compact. Finally, we have shown that if is an open limit point compact, then each of , and is an open limit point compact.Downloads
References
Adams C., and Franzosa R.,
“Introduction to Topology Pure and
Applied”, Person Printice Hall, (2008).
Munkres J. R, “Topology”, Person
Prentice Hall, Second Edition, (2009).
Morris S. A. , “Topology”, Without
Tears, Springer, New York, (2007).
Raman M., “A Pedagogical History of
Compactness”, arXiv: 1006.4131v1 ,
[math.HO] 21 Jun 22, (2010). DOI: https://doi.org/10.1002/adma.201001694
Swamy U. M., Santhi Sundar Raj Ch.,
Venkateswarlu B., and Ramesh
S., “Compactifications of an infinite
discrete space”, Int. J. Contemp. Math.
Sciences, Vol. 4, no. 22, 1079 – 1084,
(2009).
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Copyright (c) 2023 AbedalHamza Mahdi Hamza
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