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.III-24.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 product-function), the function induced on power sets by the image and inverse-image. 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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