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Spectral Reflections of Topological Spaces

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Abstract

The category Spec of spectral spaces is a reflective subcategory of the category Top of topological spaces. We compare properties of topological spaces, or of continuous maps between topological spaces, with properties of their spectral reflections. It is shown that several classical constructions with topological spaces can be produced using spectral reflections.

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Acknowledgments

Max Dickmann and Marcus Tressl have been my collaborators over several years. The present paper was developed while working on the forthcoming book [11]. Our discussions greatly influenced my view on spectral spaces and thus contributed to the ideas and results presented in this paper.

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  1. Fakultät für Informatik und Mathematik, Universität Passau, Postfach 2540, 94030, Passau, Germany

    Niels Schwartz

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  1. Niels Schwartz
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Correspondence to Niels Schwartz.

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Schwartz, N. Spectral Reflections of Topological Spaces. Appl Categor Struct 25, 1159–1185 (2017). https://doi.org/10.1007/s10485-017-9488-9

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