Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Metrics in the Cartesian Product  Part II

Stanislawa Kanas

Technical University of Rzeszow

Adam Lecko

Technical University of Rzeszow
Summary.

A continuation of [5].
It deals with the method of creation of the distance in the
Cartesian product of metric spaces. The distance between two points belonging to
Cartesian product of metric spaces has been defined as square root of the sum
of squares 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.
Examples of metric spaces defined in this way are given.
The terminology and notation used in this paper have been
introduced in the following articles
[2]
[9]
[7]
[3]
[1]
[4]
[6]
[8]

Metrics in the Cartesian product of two sets

Metrics in the Cartesian product of three sets
Bibliography
 [1]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Stanislawa Kanas, Adam Lecko, and Mariusz Startek.
Metric spaces.
Journal of Formalized Mathematics,
2, 1990.
 [5]
Stanislawa Kanas and Jan Stankiewicz.
Metrics in Cartesian product.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [8]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received July 8, 1991
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