Vol. 91, No. 2, 1980

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On the homomorphic and isomorphic embeddings of a semiflow into a radial flow

M. Edelstein

Vol. 91 (1980), No. 2, 281–291

It is the main purpose of this paper to prove the following two theorems.

Theorem I. (Isomorphism) Let (X,R+,f) be a semiflow on a separable metric space (X,d), having the properties:

  1. there is an ω X such that, for each neighborhood U of ω, there is a T R+ with f[X,t] U for all t T;
  2. for each t R+, f(,t) is a homeomorphism of X onto a closed subspace of X.

Then (X,R+,f) is isomorphic to a radial semiflow on a subset of the Hilbert Cube in l2.

Theorem II. (Homomorphism) If (X,R+,f) satisfies the hypotheses of Theorem I, with (i) replaced by

  1. ∩{f[X,t] : t 0} = {ω} for some ω X, then (X,R+,f) is homomorphic to a radial semiflow on a subset of the Hilbert Cube C and the subsemiflow induced on X∕{ω} is isomorphic to a radial semiflow in C.

Mathematical Subject Classification 2000
Primary: 54H20
Received: 27 August 1979
Published: 1 December 1980
M. Edelstein