Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Topological Properties of Subsets in Real Numbers

Konrad Raczkowski

Warsaw University, Bialystok

Pawel Sadowski

Warsaw University, Bialystok
Summary.

The following notions for real subsets are defined: open set, closed set,
compact set, intervals and neighbourhoods. In the sequel some theorems
involving above mentioned notions are proved.
Supported by RPBP.III24.C8.
MML Identifier:
RCOMP_1
The terminology and notation used in this paper have been
introduced in the following articles
[8]
[10]
[1]
[9]
[11]
[2]
[6]
[4]
[5]
[3]
[7]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Jaroslaw Kotowicz.
Convergent real sequences. Upper and lower bound of sets of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Jan Popiolek.
Some properties of functions modul and signum.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 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.
 [11]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received June 18, 1990
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