Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Submetric Spaces  Part I

Adam Lecko

Technical Univercity of Rzeszow

Mariusz Startek

Technical University of Rzeszow
Summary.

Definitions of pseudometric space, nonsymmetric metric
space, semimetric space and ultrametric space are introduced. We find some
relations between these spaces and prove that every ultrametric space is
a metric space. We define the relation {\it is between}. Moreover
we introduce the notions of the open segment and the closed segment.
Supported by RPBP.III24.B3.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[4]
[10]
[8]
[11]
[2]
[3]
[1]
[6]
[9]
[5]
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]
Stanislawa Kanas, Adam Lecko, and Mariusz Startek.
Metric spaces.
Journal of Formalized Mathematics,
2, 1990.
 [6]
Andrzej Trybulec.
Binary operations applied to functions.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [9]
Andrzej Trybulec and Czeslaw Bylinski.
Some properties of real numbers operations: min, max, square, and square root.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [11]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received September 27, 1990
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