Various types of local homogeneity

Doron Ravdin

Vol. 50 (1974), No. 2, 589–594

DOI: 10.2140/pjm.1974.50.589

Abstract

In this paper some notions of local homogeneity for metric space are investigated. A theorem on convergence of a sequence of homeomorphisms to a homeomorphism is proved and applied i.e., to show that for every two countable and dense subsets A and B of the Hilbert space l₂ there exists a homeomorphism H of l₂ onto itself such that H(A) = B.

Mathematical Subject Classification 2000

Primary: 54C10

Milestones

Received: 8 November 1972

Revised: 8 April 1973

Published: 1 February 1974