Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996
Association of Mizar Users
Components and Unions of Components

Yatsuka Nakamura

Shinshu University, Nagano

Andrzej Trybulec

Warsaw University, Bialystok
Summary.

First, we generalized {\bf skl} function for a subset of topological
spaces the value of which is the component including the set. Second,
we introduced a concept of union of components a family of which has
good algebraic properties.
At the end, we discuss relationship between connectivity of
a set as a subset in the whole space and as a subset of a subspace.
The terminology and notation used in this paper have been
introduced in the following articles
[5]
[1]
[3]
[4]
[2]

The Component of a Subset in a Topological Space

On Unions of Components

Operations Down and Up
Bibliography
 [1]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Beata Padlewska.
Connected spaces.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Beata Padlewska and Agata Darmochwal.
Topological spaces and continuous functions.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
Received February 5, 1996
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