IJPAM: Volume 89, No. 3 (2013)

CONNECTEDNESS BY CONTINUOUS
FUNCTIONS AND TEST SPACES

Richard E. Bayne$^1$, Bhamini M.P. Nayar$^2$
$^1$Department of Mathematics
Howard University
Washington, DC 20059, USA
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA


Abstract. The concept of connectedness of a set is characterized using continuous functions from the set to a Connectedness Test Space. The Connectedness Test Space is defined using the connected subsets of the set of Real Numbers, as a model. Several classical results of connectedness are proved using this approach.

Received: August 1, 2013

AMS Subject Classification: 54D05, 54C05

Key Words and Phrases: connected sets, continuous functions

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DOI: 10.12732/ijpam.v89i3.8 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 89
Issue: 3