Oriented components and their separations





separation spaces, pre-proximities, generalized topological spaces.


There is a tight connection between connectedness, connected components, and certain types of separation spaces. Recently, axiom systems for oriented connectedness were proposed leading to the notion of reaches. Here, we introduce production relations as a further generalization of connectivity spaces and reaches and derive associated systems of oriented components that generalize connected components in a natural manner. The main result is a characterization of generalized reaches in terms of equivalent separation spaces.


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Author Biography

Peter F. Stadler, Leipzig University

Department of Computer Science Full Professor


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How to Cite

B. M. R. Stadler and P. F. Stadler, “Oriented components and their separations”, Appl. Gen. Topol., vol. 18, no. 2, pp. 255–275, Oct. 2017.



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