Non-archimedean bases of topological spaces

Abstract

. Non-Archimedean bases are essential for defining and 
studying topologies that can be metrized using non-Archimedean 
metrics. A topological space is non-Archimedean metrizable if it 
admits a topology derived from a non-Archimedean metric, a metric 
satisfying the strong triangle inequality. This paper examines the role 
of non-Archimedean bases in establishing the necessary and sufficient 
conditions for a topological space to be non-Archimedean metrizable. 
Furthermore, it presents the non-Archimedean property in zero
dimensional topological spaces, emphasizing bases composed entirely 
of clopen (simultaneously open and closed) sets