Open AccessPenot’s Compactness Property in Ultrametric Spaces with an Application
Author(s) -
Mostafa Bachar,
Messaoud Bounkhel,
Samih Lazaiz
Publication year - 2021
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.579
H-Index - 28
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2021/5542843
Subject(s) - ultrametric space , compact space , completeness (order theory) , property (philosophy) , convexity , metric space , mathematics , metric (unit) , pure mathematics , discrete mathematics , mathematical analysis , philosophy , operations management , epistemology , financial economics , economics
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.