Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991
Association of Mizar Users
Paracompact and Metrizable Spaces
-
Leszek Borys
-
Warsaw University, Bialystok
Summary.
-
We give an example of a compact space.
Next we define a locally finite subset family of a topological space and
a paracompact topological space. An open sets family of a metric space we
define next and it has been shown that the metric space with any open sets
family is a topological space. Next we define metrizable space.
The terminology and notation used in this paper have been
introduced in the following articles
[12]
[4]
[14]
[1]
[13]
[8]
[6]
[10]
[7]
[5]
[11]
[15]
[2]
[3]
[9]
Contents (PDF format)
Bibliography
- [1]
Grzegorz Bancerek.
The ordinal numbers.
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]
Agata Darmochwal.
Compact spaces.
Journal of Formalized Mathematics,
1, 1989.
- [6]
Agata Darmochwal.
Families of subsets, subspaces and mappings in topological spaces.
Journal of Formalized Mathematics,
1, 1989.
- [7]
Agata Darmochwal.
Finite sets.
Journal of Formalized Mathematics,
1, 1989.
- [8]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
- [9]
Stanislawa Kanas, Adam Lecko, and Mariusz Startek.
Metric spaces.
Journal of Formalized Mathematics,
2, 1990.
- [10]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
- [11]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
- [12]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
- [13]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
- [14]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
- [15]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received June 8, 1991
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