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Compactly Generated Spaces and Quasi-spaces in Topology

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Abstract

The notions of compactness and Hausdorff separation for generalized enriched categories allow us, as classically done for the category \(\textsf {Top}\) of topological spaces and continuous functions, to study compactly generated spaces and quasi-spaces in this setting. Moreover, for a class \(\mathcal {C}\) of objects we generalize the notion of \(\mathcal {C}\)-generated spaces, from which we derive, for instance, a general concept of Alexandroff spaces. Furthermore, as done for \(\textsf {Top}\), we also study, in our level of generality, the relationship between compactly generated spaces and quasi-spaces.

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Acknowledgements

This work was developed as part of the author’s PhD thesis, under the supervision of Maria Manuel Clementino, whom the author thanks for proposing the problem of investigation, advising the whole study, and for several improvements made to the article.

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  1. CMUC, Department of Mathematics, University of Coimbra, 3001-501, Coimbra, Portugal

    Willian Ribeiro

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  1. Willian Ribeiro
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Correspondence to Willian Ribeiro.

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Communicated by Eva Colebunders.

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Research supported by Centro de Matemática da Universidade de Coimbra—UID/MAT/00324/2019 and by the FCT PhD Grant PD/BD/128059/2016, funded by the Portuguese Government through FCT/MCTES and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.

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Ribeiro, W. Compactly Generated Spaces and Quasi-spaces in Topology. Appl Categor Struct 28, 539–573 (2020). https://doi.org/10.1007/s10485-019-09589-3

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