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Composite variety-based topological theories

机译：基于复合变体的拓扑理论

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Motivated by the recent result of Rodabaugh on categorical redundancy of lattice-valued bitopology, the paper considers another viewpoint on the topic, based on the notion of composite variety-based topological theory. The new concept, apart from providing a variable-basis generalization of bitopology, incorporates the most important approaches to topology currently developed in the fuzzy community, bringing forward their categorically algebraic properties, which are cleared from point-set lattice-theoretic dependencies. Dwelling on different ways of interaction between composite topology and topology, e.g., embedding the former into the latter as a full bicoreflective subcategory, we finally arrive at the conclusion that (variable-basis) bitopological theories still deserve to be studied on their own.
机译：受Rodabaugh关于格值位学的分类冗余的最新研究结果的启发，本文基于基于复合变种的拓扑理论的概念，考虑了该主题的另一种观点。新概念除了提供可变的基础位图概括外，还结合了模糊界当前开发的最重要的拓扑方法，提出了其分类代数性质，这些性质已从点集格理论的依赖中清除。讨论复合拓扑和拓扑之间的不同交互方式，例如将前者作为完整的双核反射子类别嵌入后者，我们最终得出这样的结论，即（可变基础）比特论理论仍然值得自己研究。

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