Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990 Association of Mizar Users

Partial Functions from a Domain to a Domain


Jaroslaw Kotowicz
Warsaw University, Bialystok
Supported by RPBP.III-24.C8.

Summary.

The value of a partial function from a domain to a domain and a inverse partial function are introduced. The value and inverse function were defined in the article [1], but new definitions are introduced. The basic properties of the value, the inverse partial function, the identity partial function, the composition of partial functions, the $1{-}1$ partial function, the restriction of a partial function, the image, the inverse image and the graph are proved. Constant partial functions are introduced, too.

MML Identifier: PARTFUN2

The terminology and notation used in this paper have been introduced in the following articles [5] [7] [8] [9] [1] [2] [4] [3] [6]

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. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[4] Andrzej Trybulec. Binary operations applied to functions. Journal of Formalized Mathematics, 1, 1989.
[5] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[6] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[7] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[8] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[9] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.

Received May 31, 1990


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