Vol. 41, No. 2, 1972

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The embedding of homeomorphisms of the plane in continuous flows

Gary Douglas Jones

Vol. 41 (1972), No. 2, 421–436

A study of fundamental regions of the plane under an orientation preserving, fixed point free, self-homeomorphism of the plane is made under the conditions that there are finitely many fundamental regions Ri under f, if x Ri IntRi, then x C Ri IntRi where C is a proper flowline, and if x1 and x2 are in Int Ri, then x1 x2 mod Int Ri. The topological structure of the fundamental regions is determined. Using these results, it is shown that in certain cases the embedding problem can be reduced to a problem of extending a continuous flow defined on an open set to the closure of the set.

In the last section, sufficient conditions for self-homeomorphisms of the plane and the closed unit disc with one fixed point to be embedded in continuous flows are given.

Mathematical Subject Classification 2000
Primary: 54H20
Received: 24 October 1969
Revised: 19 October 1971
Published: 1 May 1972
Gary Douglas Jones