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

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.