On extensions of homeomorphisms to homeomorphisms

Doron Ravdin

Vol. 37 (1971), No. 2, 481–495

DOI: 10.2140/pjm.1971.37.481

Abstract

Let h;P → Q be a homeomorphism between two compact subsets of the topological spaces X and Y respectively.

Conditions on the decompositions of X∖P and Y ∖Q are found such that there exists a homeomorphism H of X onlo Y which is an extension of h.

It is shown that if P and Q are compact subsets of the one dimensional space R_ω consisting of all rational points of the Hilbert space l₂ then any homeomorphism between P and Q can be extended to a homeomorphism of R_ω onto itself. Thus an example of a one dimensional space having a very high degree of homogenity is obtained.

A generalization of a theorem of B. Knaster and M. Reichbach (Reichaw) is also given.

Mathematical Subject Classification 2000

Primary: 54C20

Milestones

Received: 1 September 1970

Revised: 13 January 1971

Published: 1 May 1971