Algebraic representation of continuous lattices via the open filter monad, revisited

TL;DR

This paper revisits Day's algebraic approach to continuous lattices, clarifying the connection between continuous lattices and the open filter monad in the context of $T_0$ spaces.

Contribution

It provides a clearer and more accessible presentation of Day's original method linking continuous lattices with the open filter monad.

Findings

Continuous lattices are characterized as algebras of the open filter monad.

The paper clarifies the process of Day's approach.

It enhances understanding of the algebraic structure of continuous lattices.

Abstract

In [A. Day, Filter monads, continuous lattices and closure systems, Can. J. Math. 27 (1975) 50--59], Day showed that continuous lattices are precisely the algebras of the open filter monad over the category of $T_0$ spaces. The aim of this paper is to give a clean and clear version of the whole process of Day's approach.