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arXiv · 2410.04674

The bounded ideal monad on the category of quasi-metric spaces and its algebras

Kai Wang·Dexue Zhang
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Abstract

The notion of bounded ideals is introduced for quasi-metric spaces. Such ideals give rise to a monad, the bounded ideal monad, on the category of quasi-metric spaces and non-expansive maps. Algebras of this monad are metric version of local dcpos of Mislove. It is shown that an algebra of the bounded ideal monad is a standard quasi-metric space of which the formal balls form a local dcpo; and that a continuous algebra is a standard quasi-metric space of which the formal balls form a local domain.

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Kai Wang, Dexue Zhang. 2024-10-07. The bounded ideal monad on the category of quasi-metric spaces and its algebras. https://arxiv.org/abs/2410.04674

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