On Pseudo-Category of Quasi-Isotone Spaces

DOI: 10.4236/apm.2014.42009   PDF   HTML   XML   2,859 Downloads   4,162 Views  

Abstract

Recent developments in mathematics have in a sense organized objects of study into categories, where properties of mathematical systems can be unified and simplified through presentation of diagrams with arrows. A category is an algebraic structure made up of a collection of objects linked together by morphisms. Category theory has been advanced as a more concrete foundation of mathematics as opposed to set-theoretic language. In this paper, we define a pseudo-category on the class of isotonic spaces on which the idempotent axiom of the Kuratowski closure operator is assumed.

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H. Were, S. Gathigi, P. Otieno, M. Gichuki and K. Sogomo, "On Pseudo-Category of Quasi-Isotone Spaces," Advances in Pure Mathematics, Vol. 4 No. 2, 2014, pp. 59-61. doi: 10.4236/apm.2014.42009.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] W. J. Thron, “What Results Are Valid on Cech-Closure Spaces,” Topology Proceedings, Vol. 6, No. 3, 1981, pp. 135-158.
[2] T. A Sunitha, “A Study of Cech Closure Spaces,” Doctor of Philosophy Thesis, School of Mathematical Sciences, Cochin University of Science and Technology, Cochin, 1994.
[3] A. K. Elzenati and E. D. Habil, “Connectedness in Isotonic Spaces,” Turkish Journal of Mathematics, Vol. 30, No. 3, 2006, pp. 247-262.
[4] C. McLarty, “Elementary Categories, Elementary Toposes,” Oxford University Press, Oxford, 1992.
[5] S. MacLane, “Category for the Working Mathematician,” 2nd Edition, Springer-Verlag Inc., New York, 1998.

  
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