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Transformations on the product of Grassmann spaces

Hans Havlicek, Mark Pankov

Abstract

We describe all adjacency preserving bijections of certain products of Grassmann spaces.

Transformations on the product of Grassmann spaces

Abstract

We describe all adjacency preserving bijections of certain products of Grassmann spaces.

Paper Structure

This paper contains 5 sections, 11 theorems, 33 equations.

Table of Contents

  1. Introduction
  2. A- transformations and C- transformations
  3. Proof of Theorem \ref{['thm:C']}
  4. Proof of Theorem \ref{['thm:A']}
  5. Proofs of Theorem \ref{['thm:CGxG']} and Theorem \ref{['thm:AGxG']}

Key Result

Theorem 1

Every closeness preserving transformation of ${\mathcal{G}}$ is one of the mappings considered in Examples exmp:1--exmp:n=2. Hence it is an adjacency preserving transformation.

Theorems & Definitions (25)

  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Theorem 1
  • Theorem 2
  • Example 5
  • Theorem 3
  • Example 6
  • Theorem 4
  • ...and 15 more