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Extended topology and systems

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Abstract

In this paper is indicated the possible utility of isotonic spaces as a background language for discussing systems. In isotonic spaces the basic duality between “neighborhood” and “convergent” first achieves a proper background permitting applications beyond the scope of topological spaces. A generalization of continuity of mappings based on ancestral relations is presented and this definition is applied to establish a necessary and sufficient condition that mappings preserve connectedness. Fortunately for systems theory, it is not necessary to have infinite sets or infinitary operators to apply definitions of neighborhood, convergents, continuity and connectedness.

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References

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  2. Preston C. Hammer, Isotonic spaces in convexity, (to appear in the Proceedings of a Colloquium on Convexity held in Copenhagen in 1965).

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Authors and Affiliations

  1. Computer Science Department, Pennsylvania State University, USA

    Preston C. Hammer

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  1. Preston C. Hammer
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This work was supported in part by a grant from the National Science Foundation.

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Hammer, P.C. Extended topology and systems. Math. Systems Theory 1, 135–142 (1967). https://doi.org/10.1007/BF01705523

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  • DOI: https://doi.org/10.1007/BF01705523

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