Applications of sequential spaces to Smyth power spaces and sober spaces

Zhengmao He

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arXiv · 2609.27775

Applications of sequential spaces to Smyth power spaces and sober spaces

Zhengmao He

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Abstract

Recently, in the study of topological properties in Domain theory, the first countable spaces and Frechet-Urysohn spaces receive close attention and are frequently employed. In this paper, we focus on sequential spaces weaker than Frechet-Urysohn spaces. The main results are: (1) For a well-filtered space X, the Scott topology and the upper vietoris topology on K(X) coincide if PS(X) is a sequential space; (2) every ω-well-filtered coherent d- space X is sober when the procuct of X is a sequential space.

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Zhengmao He. 2026-08-17. Applications of sequential spaces to Smyth power spaces and sober spaces. https://arxiv.org/abs/2609.27775

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