Titlebook: Advances in Topology and Their Interdisciplinary Applications; Santanu Acharjee Book 2023 The Editor(s) (if applicable) and The Author(s),

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commute

,Contra Continuity Properties of?Relations in?Relator Spaces,the inverse image ?. ?is a closed subset of ?.. This seems to be a rather inconvenient continuity-like property. However, despite this, it has been intensively investigated by a surprisingly great number of prominent mathematicians. Therefore, it seems reasonable to treat this notion in relator spac

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oxidant

,Representations of?Preference Relations with?Preutility Functions on?Metric Spaces,ences theorems rely on Debreu-Eilenberg’s theorems through abstract mathematics based on topological properties. We adopt another approach starting from metric spaces instead. We obtain representation theorems of preference relations with bivariate functions. This allows us to handle intransitivitie

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,Filter Versus Ideal on?Topological Spaces,terms of a filter. To do this, the big set (resp., small set) and homeomorphism are essential parts. As an application of one of our results, we develop a secret information-sharing scheme in?topological cryptography. This new secret-sharing scheme is developed for secret information sharing between

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