Barisan Cauchy pada Ruang Semimetrik Terbatas - Rianjaya, Ilham Dangu; Putri, Amelia; Musthofa, Syarto (JOSTECH Journal of Science and Technology, 2024)
Semimetric spaces with bounded property means that it is bounded below and bounded above by constant multiples of a metric space. Moreover, in semimetric spaces, every convergent sequence is not necessarily to be a Cauchy sequence. This study aims to examine the property of sequences of semimetric spaces with boundary property. In this work, analytical method of proof is used. The results obtained are the equivalence of the convergence of the sequence, and the fulfillment of the Cauchy criterion in the finite semimetric space and the metric space that bounds it. In addition, the completeness property in one space also causes the other space to fulfill the completeness property.