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

Affiliation(s)
Department of Mathematics, Egerton University, Egerton, Kenya.

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.

KEYWORDS
Closure Operator; Isotonic Space; Quasi-Isotone Spaces; Pseudo-Category

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.

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.