Vol. 37, No. 2, 1971

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On extensions of homeomorphisms to homeomorphisms

Doron Ravdin

Vol. 37 (1971), No. 2, 481–495

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

Conditions on the decompositions of XP 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 Rω consisting of all rational points of the Hilbert space l2 then any homeomorphism between P and Q can be extended to a homeomorphism of Rω 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
Received: 1 September 1970
Revised: 13 January 1971
Published: 1 May 1971
Doron Ravdin