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.III-24.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
[
Download a postscript version,
MML identifier index,
Mizar home page]