Journal of Formalized Mathematics
Volume 13, 2001
University of Bialystok
Copyright (c) 2001 Association of Mizar Users

On Cosets in Segre's Product of Partial Linear Spaces


Adam Naumowicz
University of Bialystok

Summary.

This paper is a continuation of [15]. We prove that the family of cosets in the Segre's product of partial linear spaces remains invariant under automorphisms.

MML Identifier: PENCIL_2

The terminology and notation used in this paper have been introduced in the following articles [19] [10] [23] [2] [24] [16] [7] [9] [8] [5] [13] [1] [4] [3] [17] [20] [21] [6] [11] [25] [14] [18] [12] [22] [15]

Contents (PDF format)

  1. Preliminaries on Finite Sequences
  2. Segre Cosets
  3. Collineations of Segre Product

Bibliography

[1] Grzegorz Bancerek. Cardinal numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[3] Grzegorz Bancerek. K\"onig's theorem. Journal of Formalized Mathematics, 2, 1990.
[4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Journal of Formalized Mathematics, 1, 1989.
[5] Jozef Bialas. Group and field definitions. Journal of Formalized Mathematics, 1, 1989.
[6] Ewa Burakowska. Subalgebras of many sorted algebra. Lattice of subalgebras. Journal of Formalized Mathematics, 6, 1994.
[7] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[8] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[9] Czeslaw Bylinski. Partial functions. Journal of Formalized Mathematics, 1, 1989.
[10] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[11] Agata Darmochwal. Families of subsets, subspaces and mappings in topological spaces. Journal of Formalized Mathematics, 1, 1989.
[12] Agata Darmochwal and Yatsuka Nakamura. The topological space $\calE^2_\rmT$. Arcs, line segments and special polygonal arcs. Journal of Formalized Mathematics, 3, 1991.
[13] Jaroslaw Kotowicz. Functions and finite sequences of real numbers. Journal of Formalized Mathematics, 5, 1993.
[14] Beata Madras. Product of family of universal algebras. Journal of Formalized Mathematics, 5, 1993.
[15] Adam Naumowicz. On Segre's product of partial line spaces. Journal of Formalized Mathematics, 12, 2000.
[16] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.
[17] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.
[18] Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Journal of Formalized Mathematics, 11, 1999.
[19] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[20] Andrzej Trybulec. Many-sorted sets. Journal of Formalized Mathematics, 5, 1993.
[21] Andrzej Trybulec. Many sorted algebras. Journal of Formalized Mathematics, 6, 1994.
[22] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[23] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[24] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[25] Mariusz Zynel and Adam Guzowski. \Tzero\ topological spaces. Journal of Formalized Mathematics, 6, 1994.

Received August 14, 2001


[ Download a postscript version, MML identifier index, Mizar home page]