TITLE:
On the Behavior of Connectedness Properties in Isotonic Spaces under Perfect Mappings
AUTHORS:
Stephen M. Gathigi, Moses N. Gichuki, Kewamoi C. Sogomo
KEYWORDS:
Closure Operator; Closure Axiom; Isotonic Space; Perfect Mapping; Connectedness
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.9,
December
2,
2013
ABSTRACT: The topological study of connectedness is heavily geometric or visual. Connectedness and connectedness-like properties play an important role in most topological characterization theorems, as well as in the study of obstructions to the extension of functions. In this paper, the behaviour of these properties in the realm of closure spaces is investigated using the class of perfect mappings. A perfect mapping is a type of map under which the image generally inherits the properties of the mapped space. It turns out that the general behaviour of connectedness properties in topological spaces extends to the class of isotone space.