Oriented components and their separations

Baerbel M R Stadler; Peter F. Stadler

doi:10.4995/agt.2017.5868

Authors

Baerbel M R Stadler Max Planck Institute for Mathematics in the Sciences
Peter F. Stadler Leipzig University https://orcid.org/0000-0002-5016-5191

DOI:

https://doi.org/10.4995/agt.2017.5868

Keywords:

separation spaces, pre-proximities, generalized topological spaces.

Abstract

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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