Vol. 70, No. 1, 1977

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Polychronis Strantzalos

Vol. 70 (1977), No. 1, 253–267

The strictly almost equicontinuous actions (SAE-actions) are characterized with notions from the theory of proper actions (P-actions). Roughly speaking we prove that every SAE-action is a restriction of a P-action. Through this characterization we are able:

(1) To improve known results of the theory of SAE-actions and to get new ones concerning the structure of the acting group and the (phase) space.

(2) To classify all SAE-actions, which extend a given equicontinuous action.

The more general assumptions on the space, under which the theory of SAE-actions works, provided the motivation to refine and improve upon the corresponding assumptions of the theory of P-actions.

Mathematical Subject Classification 2000
Primary: 54H15
Secondary: 57E10
Received: 6 February 1976
Revised: 28 January 1977
Published: 1 May 1977
Polychronis Strantzalos