Penot's Compactness Property in Ultrametric Spaces with an Application

Mostafa Bachar, Messaoud Bounkhel, Samih Lazaiz, Shanhe Wu
2021 Journal of Function Spaces  
In this work, we investigate the compactness property in the sense of Penot in ultrametric spaces. Then, we show that spherical completeness is exactly the Penot's compactness property introduced for convexity structures. The spherical completeness property misled some mathematicians to it to hyperconvexity in metric spaces. As an application, we discuss some fixed point results in spherically complete ultrametric spaces.
doi:10.1155/2021/5542843 fatcat:cnmww5gmlvfhra52kn5abtxqf4