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Metric Spaces – Basic Concepts, Complete Metric Spaces
Concise Introduction to Basic Real Analysis, 2019H. Dutta, P. Natarajan, Y. Cho
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COMPLETENESS IN MULTI METRIC SPACES
South East Asian J. of Mathematics and Mathematical Sciences, 2022In the present paper a notion of convergence in multi metric space is presented. Complete multi metric space is introduced and some properties are studied. Cantor’s intersection theorem and Banach’s fixed point theorem are es- tablished in multi set settings.
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Complete Metric Spaces: A Survey
Revista Review Index Journal of MultidisciplinaryComplete metric spaces are highly important not only in mathematical theories but also in control system engineering, signal processing, machine learning, data science, etc. Completion of metric space plays a very important role in the fixed point theory.
Ajit Kumar Gupta, Jayesh J. Patel
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1997
Abstract It is easy to show that a convergent sequence is a Cauchy sequence. Also, a Cauchy sequence converges if, and only if, it contains a convergent subsequence.
Reinhold Meise, Dietmar Vogt
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Abstract It is easy to show that a convergent sequence is a Cauchy sequence. Also, a Cauchy sequence converges if, and only if, it contains a convergent subsequence.
Reinhold Meise, Dietmar Vogt
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NOTES ON ORTHOGONAL-COMPLETE METRIC SPACES
Bulletin of the Australian Mathematical Society, 2021AbstractWe prove that the restriction of a given orthogonal-complete metric space to the closure of the orbit induced by the origin point with respect to an orthogonal-preserving and orthogonal-continuous map is a complete metric space. Then we show that many existence results on fixed points in orthogonal-complete metric spaces can be proved by using ...
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COMPLETIONS OF PRODUCTS OF METRIC SPACES
The Quarterly Journal of Mathematics, 1992Completeness and completions are described for spaces from the epireflective hull of pseudometric spaces (infinite values are allowed) in approach spaces. For metric spaces they coincide with the known concepts; every completely regular space is complete.
Lowen, Robert, Robeys, Kristin
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ON THE COMPLETION OF -METRIC SPACES
Bulletin of the Australian Mathematical Society, 2018Based on the metrisation of$b$-metric spaces of Paluszyński and Stempak [‘On quasi-metric and metric spaces’,Proc. Amer. Math. Soc.137(12) (2009), 4307–4312], we prove that every$b$-metric space has a completion. Our approach resolves the limitation in using the quotient space of equivalence classes of Cauchy sequences to obtain a completion of a$b ...
NGUYEN VAN DUNG, VO THI LE HANG
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2009
Abstract We saw in Chapter 4 how useful the completeness property of R is. From a theoretical viewpoint, completeness lets us solve equations such as x = 2 in R which have no solution in Q. Here is a practical version of the same phenomenon; we shall refer back to it a couple of times in this chapter.
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Abstract We saw in Chapter 4 how useful the completeness property of R is. From a theoretical viewpoint, completeness lets us solve equations such as x = 2 in R which have no solution in Q. Here is a practical version of the same phenomenon; we shall refer back to it a couple of times in this chapter.
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Complete probabilistic metric spaces
Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1971Menger [4] initiated the study of probabilistic metric spaces in 1942. A probabilistic metric space (briefly a PM space) is a space in which the "distance" between any two points is a probability distribution function. These spaces are assumed to satisfy axioms which are quite similar to the axioms satisfied in an ordinary metric space.
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