Uniform ball structures

• Date: 2018
• Main Author: Protasov, I. V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: ball structure; metrizability; 03E99; 54A05; 54E15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1145
• Journal Title: Algebra and Discrete Mathematics

A ball structure is a triple \(\mathbb B=(X,P,B)\), where \(X,P\) are nonempty sets and, for all  \(x\in X\), \(\alpha \in P\), \(B(x,\alpha )\) is a subset of \(X, x\in B(x,\alpha )\), which is called a ball of radius \(\alpha \) around \(x\). We introduce the class of uniform ball structures as an...