We use the theory of triposes to prove that every (non-degenerate) locale H is the set of truth values of a complete and co-complete quasi-topos into which the category of topological spaces embeds and the topos of sheaves over H reflectively embeds.
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The author wants to thank Professors M. E. Maietti, G. Rosolini and T. Streicher for their useful comments and also the anonymous readers whose advices considerably improved the final shape of the paper.
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Pasquali, F. On a Generalization of Equilogical Spaces. Log. Univers. 12, 129–140 (2018). https://doi.org/10.1007/s11787-018-0192-9
- Partial equivalence relations
- Equilogical spaces
Mathematics Subject Classification
- Primary 03G30
- Secondary 03B20