Metrics in Cartesian Product

Stanislawa Kanas

Technical Univercity of Rzeszow

Jan Stankiewicz

Technical University of Rzeszow

Summary.

A continuation of paper [6]. It deals with the method of creation of the distance in the Cartesian product of metric spaces. The distance of two points belonging to Cartesian product of metric spaces has been defined as sum of distances of appropriate coordinates (or projections) of these points. It is shown that product of metric spaces with such a distance is a metric space.

Supported by RPBP.III-24.B3.

MML Identifier: METRIC_3

Contents (PDF format)

Bibliography

[1] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.

[2] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[5] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.

[6] Stanislawa Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Journal of Formalized Mathematics, 2, 1990.

[7] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[8] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.

[9] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.

[10] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.