Affiliations: [a] School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, 273165, China. longchunw@163.com | [b] College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410012, China. lankun.guo@gmail.com | [c] School of Mathematics, Hunan University, Changsha, Hunan, 410082, China. liqingguoli@aliyun.com
Correspondence:
[†]
Address for correspondence: College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan, 410012, China; School of Mathematics, Hunan University, Changsha, Hunan, 410082, China.
Note: [*] This work is supported by the National Natural Science Foundation of China (No. 11771134); Outstanding Youth Foundation of Hunan Scientific Committee (No. 2019JJ30016); Key Programs of Hunan Education Committee (No. 20A301).
Abstract: Formal Concept Analysis (FCA) has been proven to be an effective method of restructuring complete lattices and various algebraic domains. In this paper, the notion of contractive mappings over formal contexts is proposed, which can be viewed as a generalization of interior operators on sets into the framework of FCA. Then, by considering subset-selections consistent with contractive mappings, the notions of attribute continuous formal contexts and continuous concepts are introduced. It is shown that the set of continuous concepts of an attribute continuous formal context forms a continuous domain, and every continuous domain can be restructured in this way. Moreover, the notion of F-morphisms is identified to produce a category equivalent to that of continuous domains with Scott continuous functions. The paper also investigates the representations of various subclasses of continuous domains including algebraic domains and stably continuous semilattices.
