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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