Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
Basic Functions and Operations on Functions

Czeslaw Bylinski

Warsaw University, Bialystok

Supported by RPBP.III24.C1.
Summary.

We define the following mappings:
the characteristic function of a subset of a set,
the inclusion function (injection or embedding),
the projections from a
Cartesian product onto its arguments and diagonal function (inclusion
of a set into its Cartesian square).
Some operations
on functions are also defined: the products of two functions
(the complex function and
the more general productfunction), the function induced on power sets
by the image and inverseimage.
Some simple propositions
related to the introduced notions are proved.
MML Identifier:
FUNCT_3
The terminology and notation used in this paper have been
introduced in the following articles
[4]
[3]
[5]
[6]
[7]
[1]
[2]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [4]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [5]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
Received May 9, 1989
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