Journal of Formalized Mathematics
Volume 6, 1994
University of Bialystok
Copyright (c) 1994 Association of Mizar Users

On the Decomposition of the Continuity

Marian Przemski
Warsaw University, Bialystok


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

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

Contents (PDF format)


The author wishes to thank Professor A. Trybulec for many helpful talks during the preparation of this paper.


[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.

Received December 12, 1994

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