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arXiv · 2211.16133

Further studies on open well-filtered spaces

Chong Shen·Xiaoyong Xi·Dongsheng Zhao
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Abstract

The open well-filtered spaces were introduced by Shen, Xi, Xu and Zhao to answer the problem whether every core-compact well-filtered space is sober. In the current paper we explore further properties of open well-filtered spaces. One of the main results is that if a space is open well-filtered, then so is its upper space (the set of all nonempty saturated compact subsets equipped with the upper Vietoris topology). Some other properties on open well-filtered spaces are also studied.

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Chong Shen, Xiaoyong Xi, Dongsheng Zhao. 2022-11-29. Further studies on open well-filtered spaces. https://doi.org/10.46298/entics.10392

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