On Pseudo-Category of Quasi-Isotone Spaces

Author(s)
Hezron S. Were^{*},
Stephen M. Gathigi,
Paul A. Otieno,
Moses N. Gichuki,
Kewamoi C. Sogomo

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.

Cite this paper

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.

H. Were, S. Gathigi, P. Otieno, M. Gichuki and K. Sogomo, "On Pseudo-Category of Quasi-Isotone Spaces,"

References

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[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.

[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.