Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Filters, topologies, the Rado graph and the Urysohn space

Peter J. Cameron

Abstract

My work with Anatoly Vershik concerned automorphism groups of the Rado graph and homeomorphism groups of the Urysohn space. This paper contains some further thoughts on these issues, together with connections to topologies and filters on countable sets.

Filters, topologies, the Rado graph and the Urysohn space

Abstract

My work with Anatoly Vershik concerned automorphism groups of the Rado graph and homeomorphism groups of the Urysohn space. This paper contains some further thoughts on these issues, together with connections to topologies and filters on countable sets.
Paper Structure (6 sections, 6 theorems, 1 equation)

This paper contains 6 sections, 6 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. Imprimitive groups and topologies
  3. Topologies and filters
  4. Mekler's theorem
  5. Neighbourhood filters
  6. Acknowledgement

Key Result

Proposition 2.1

Let $G$ be a transitive permutation group on $\Omega$. Then $G$ is primitive if and only if every non-trivial $G$-invariant topology is T0, and $G$ is strongly primitive if and only if every non-trivial $G$-invariant topology is T1.

Theorems & Definitions (8)

  • Proposition 2.1
  • Theorem 3.1
  • Proposition 4.1
  • Proof 1
  • Theorem 4.2
  • Proposition 5.1
  • Theorem 5.2
  • Proof 2