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Concentrated nearness spaces

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Categorical Topology

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 719))

Abstract

The category RoTop of topological Ro-spaces and continuous maps can be embedded as a nice subcategory into Near, the category of nearness spaces and nearness preserving maps. The resulting subcategory TNear of Near has the property that products and subspaces of TNear-objects taken in Near are generally different from those taken in TNear. This led H.Herrlich — who introduced nearness spaces — to the problem to characterize those spaces belonging to the epireflective hull EH(TNear) of TNear in Near internally, which is still open.

In this paper we introduce the property of being "concentrated" for nearness spaces, which gives rise to a subcategory of Near that contains all subtopological nearness spaces of Bentley and contributes to the problem mentioned above in the sense that it is the largest subcategory of EH(TNear) known so far for which an internal characterization exists. We discuss properties of these spaces and show that they may be helpful in solving Herrlich's problem, but are also interesting in their own right.

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Authors and Affiliations

  1. Zentralblatt für Mathematik, Otto-Suhr-Allee 26, D - 1000, Berlin 10

    N. C. Heldermann

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  1. N. C. Heldermann
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Horst Herrlich Gerhard Preuß

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© 1979 Springer-Verlag

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Heldermann, N.C. (1979). Concentrated nearness spaces. In: Herrlich, H., Preuß, G. (eds) Categorical Topology. Lecture Notes in Mathematics, vol 719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065265

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  • DOI: https://doi.org/10.1007/BFb0065265

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09503-3

  • Online ISBN: 978-3-540-35193-1

  • eBook Packages: Springer Book Archive

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