Abstract
AbstractSobriety, well-filteredness, and monotone convergence are three of the most important properties of topological spaces extensively studied in domain theory. Some other weak forms of sobriety and well-filteredness have also been investigated by some authors. In this paper, we introduce the notion of Θ-fine spaces, which provides a unified approach to such properties. In addition, this general approach leads to the definitions of some new topological properties.
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