Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 19, No. 2, pp. 101-165 (2003)

Well-chainedness and connectedness

G. Pataki and Á. Száz

University of Debrecen, Hungary

Abstract: A unified treatment of some old and new well-chainedness and connectedness properties of the most basic topological structures (such as closures, proximities and uniformities, for instance) is offered in the framework of relators (families of binary relations) and their fundamental refinements.

The results obtained show that the various connectedness properties are actually particular cases of Cantor's well-chainedness property neglected by several authors. Moreover, they show that the hyperconnectedness introduced by L. A. Steen and J. A. Seebach is a particular case of our paratopological connectedness.

Keywords: Operations on relators (relational systems), well-chainedness and connectedness properties of relators.

Classification (MSC2000): 54D05

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