Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

Algebraic Operation on Subsets of Many Sorted Sets


Agnieszka Julia Marasik
Warsaw University, Bialystok

MML Identifier: CLOSURE3

The terminology and notation used in this paper have been introduced in the following articles [13] [5] [16] [12] [17] [2] [4] [3] [7] [6] [14] [15] [1] [10] [8] [9] [11]

Contents (PDF format)

  1. Preliminaries
  2. Relationships between Subsets Families
  3. Algebraic Operation on Subsets of Many Sorted Sets

Bibliography

[1] Ewa Burakowska. Subalgebras of many sorted algebra. Lattice of subalgebras. Journal of Formalized Mathematics, 6, 1994.
[2] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. The modification of a function by a function and the iteration of the composition of a function. Journal of Formalized Mathematics, 2, 1990.
[7] Agata Darmochwal. Finite sets. Journal of Formalized Mathematics, 1, 1989.
[8] Artur Kornilowicz. Certain facts about families of subsets of many sorted sets. Journal of Formalized Mathematics, 7, 1995.
[9] Artur Kornilowicz. Definitions and basic properties of boolean and union of many sorted sets. Journal of Formalized Mathematics, 7, 1995.
[10] Artur Kornilowicz. On the closure operator and the closure system of many sorted sets. Journal of Formalized Mathematics, 8, 1996.
[11] Yatsuka Nakamura, Piotr Rudnicki, Andrzej Trybulec, and Pauline N. Kawamoto. Preliminaries to circuits, I. Journal of Formalized Mathematics, 6, 1994.
[12] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[13] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[14] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[15] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[16] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[17] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

Received June 23, 1997

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