
Contents
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Abstract Abstract
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12.1 Introduction 12.1 Introduction
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12.2 A Categorical View of Basic Pairs 12.2 A Categorical View of Basic Pairs
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12.3 The Characterization 12.3 The Characterization
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12.4 Comparison with the Presentations of Formal Topologies 12.4 Comparison with the Presentations of Formal Topologies
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Acknowledgements Acknowledgements
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References References
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Cite
Abstract
The constructive approach to topology has produced a wealth of new insights about spaces, almost reaching the point of making these more elementary than sets. In particular, the point of view taken by the notion of the basic picture as developed in the context of formal topology brings forward the relevance of relations between sets as an elementary constituent for understanding topological spaces. The chapter employs the language and notions of category theory to put the concept of the basic pair under scrutiny. It gives a presentation of topological spaces, which exploits another monoidal structure on the category of complete sup-lattices compared with the one given by Galois connections as in the memoirs by Joyal and Tierney. In this modified context, this chapter characterizes the frames which are topologies.
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