D-completion, well-filterification and sobrification

Hualin Miao; Longchun Wang; Qingguo Li

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arXiv · 2101.04894

D-completion, well-filterification and sobrification

Hualin Miao·Longchun Wang·Qingguo Li

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Abstract

In this paper, we obtain some sufficient conditions for the D-completion of a T0 space to be the well-filterification of this space, the well-filterification of a T0 space to be the sobrification of this space and the D-completion of a T0 space to be the sobrification, respectively. Moreover, we give an example to show that a tapered closed set may be neither the closure of a directed set nor the closed KF-set, respectively. Because the tapered closed set is a closed WD-set, the example also gives a negative answer to a problem proposed by Xu. Meantime, a new direct characterization of the D-completion of a T0 space is given by using the notion of pre-c-compact elements.

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BibTeX RIS

Hualin Miao, Longchun Wang, Qingguo Li. 2021-01-13. D-completion, well-filterification and sobrification. https://arxiv.org/abs/2101.04894

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