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.

#### MML Identifier: CONNSP_3

The terminology and notation used in this paper have been introduced in the following articles [5] [1] [3] [4] [2]

#### Contents (PDF format)

1. The Component of a Subset in a Topological Space
2. On Unions of Components
3. 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.