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Compactification with Respect to a Generalized-net Convergence on Constructs

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Abstract

We introduce and deal with a convergence on (objects of) constructs which is expressed in terms of generalized nets. The generalized nets used are obtained from the usual nets by replacing the construct of directed sets and cofinal maps by an arbitrary construct. Convergence separation and convergence compactness are then introduced in a natural way. We study the convergence compactness and compactification and show that they behave in much the same way as the compactness and compactification of topological spaces.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Brno, 616 69, Brno, Czech Republic

    Josef Šlapal

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  1. Josef Šlapal
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Correspondence to Josef Šlapal.

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Partially supported by Ministry of Education of the Czech Republic, research plan no. MSM0021630518.

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Šlapal, J. Compactification with Respect to a Generalized-net Convergence on Constructs. Appl Categor Struct 19, 523–537 (2011). https://doi.org/10.1007/s10485-009-9205-4

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