β$-和λ$-映射的一般化

arXiv - MATH - General Topology Pub Date : 2024-07-24 DOI:arxiv-2407.16941

Ana Belén Avilez

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引用次数: 0

摘要

我们将$\beta$-和$\lambda$-映射的概念概括为子局部的一般选择，从而得到了不同类别的局部映射。这些新的映射类别被用来描述几乎正态性、极端不连接性、$F$-框架、$Oz$-框架以及其他类型的局域，其方法类似于通过$\beta$映射描述正态局域。作为一个副产品，我们得到了保留完全低于关系（即断言框架同构的右邻接）的局部映射的特征。

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Generalizing $β$- and $λ$-maps

We generalize the notions of $\beta$- and $\lambda$-maps to general selections of sublocales, obtaining different classes of localic maps. These new classes of maps are used to characterize almost normality, extremal disconnectedness, $F$-frames, $Oz$-frames, among others types of locales, in a manner akin to the characterization of normal locales via $\beta$-maps. As a byproduct we obtain a characterization of localic maps that preserve the completely below relation (that is, the right adjoints of assertive frame homomorphisms).

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arXiv - MATH - General Topology

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