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.

Received February 5, 1996


[ Download a postscript version, MML identifier index, Mizar home page]