Journal of Formalized Mathematics
Volume 8, 1996
University of Bialystok
Copyright (c) 1996 Association of Mizar Users

More on the Lattice of Many Sorted Equivalence Relations


Robert Milewski
Warsaw University, Bialystok

MML Identifier: MSUALG_7

The terminology and notation used in this paper have been introduced in the following articles [18] [6] [20] [21] [3] [5] [4] [17] [16] [19] [22] [1] [8] [7] [13] [2] [11] [12] [14] [15] [9] [10]

Contents (PDF format)

  1. Lattice of Many Sorted Equivalence Relations is Complete
  2. Sublattices inheriting SUP's and INF's
  3. Segment of Real Numbers as a Complete Lattice

Bibliography

[1] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[2] Ewa Burakowska. Subalgebras of many sorted algebra. Lattice of subalgebras. Journal of Formalized Mathematics, 6, 1994.
[3] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[7] Marek Chmur. The lattice of real numbers. The lattice of real functions. Journal of Formalized Mathematics, 2, 1990.
[8] Marek Chmur. The lattice of natural numbers and the sublattice of it. The set of prime numbers. Journal of Formalized Mathematics, 3, 1991.
[9] Artur Kornilowicz. Certain facts about families of subsets 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] Malgorzata Korolkiewicz. Homomorphisms of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[12] Malgorzata Korolkiewicz. Many sorted quotient algebra. Journal of Formalized Mathematics, 6, 1994.
[13] Beata Madras. Products of many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[14] Robert Milewski. Lattice of congruences in many sorted algebra. Journal of Formalized Mathematics, 8, 1996.
[15] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[16] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.
[17] Konrad Raczkowski and Pawel Sadowski. Topological properties of subsets in real numbers. Journal of Formalized Mathematics, 2, 1990.
[18] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[19] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[20] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[21] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[22] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received February 9, 1996

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