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
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.
The terminology and notation used in this paper have been
introduced in the following articles
[3]
[1]
[2]
[4]
Contents (PDF format)
Acknowledgments
The author wishes to thank Professor A. Trybulec for many helpful
talks during the preparation of this paper.
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.
Received December 12, 1994
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