On the Decomposition of the Continuity

Marian Przemski

Warsaw University, Bialystok

Summary.

This article is devoted to functions of general topological spaces. A function from $X$ to $Y$ is $A$-continuous if the counterimage of every open set $V$ of $Y$ belongs to $A$, where $A$ is a collection of subsets of $X$. We give the following characteristics of the continuity, called decomposition of continuity: A function $f$ is continuous if and only if it is both $A$-continuous and $B$-continuous.

MML Identifier: DECOMP_1

Contents (PDF format)

Acknowledgments

Bibliography

[1] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[2] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.

[3] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[4] Miroslaw Wysocki and Agata Darmochwal. Subsets of topological spaces. Journal of Formalized Mathematics, 1, 1989.