On the Behavior of Connectedness Properties in Isotonic Spaces under Perfect Mappings

DOI: 10.4236/apm.2013.39093   PDF   HTML   XML   2,523 Downloads   3,847 Views  

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.

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S. Gathigi, M. Gichuki and K. Sogomo, "On the Behavior of Connectedness Properties in Isotonic Spaces under Perfect Mappings," Advances in Pure Mathematics, Vol. 3 No. 9, 2013, pp. 689-691. doi: 10.4236/apm.2013.39093.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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