Barisan Cauchy pada Ruang Semimetrik Terbatas

Ilham Dangu Rianjaya, Amelia Putri, Syarto Musthofa

Abstract


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.

Keywords


Cauchy sequence; convergent sequence; semimetric spaces; metric spaces

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DOI: https://doi.org/10.15548/jostech.v4i1.8234
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References


M. O’Searcoid, Metric spaces. Springer Science & Business Media, 2006.

W. A. Wilson, “On semi-metric spaces,” American Journal of Mathematics, vol. 53, no. 2, hlm. 361–373, 1931.

A. Branciari, “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces,” Publ. Math. Debrecen, vol. 57, no. 1–2, hlm. 31–37, 2000.

Z. Kadelburg dan S. Radenovic, “On generalized metric spaces: a survey,” TWMS Journal of Pure and Applied Mathematics, vol. 5, no. 1, hlm. 3–13, 2014.

S. Czerwik, “Contraction mappings in $ b $-metric spaces,” Acta mathematica et informatica universitatis ostraviensis, vol. 1, no. 1, hlm. 5–11, 1993.

R. Fagin dan R. Kumar, “Comparing top k lists,” SIAM Journal on discrete mathematics, vol. 17, no. 1, hlm. 134–160, 2003.

W. Kirk dan N. Shahzad, “Fixed points and Cauchy sequences in semimetric spaces,” Journal of Fixed Point Theory and Applications, vol. 17, hlm. 541–555, 2015.


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