Rectangular conditions in products and equivariant completions

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• 作者：K.L. Kozlov ^{kkozlov@mech.math.msu.su}
• 关键词：54H15 ; 54D35 ; 54E15
• 刊名：Topology and its Applications
• 出版年：2012
• 出版时间：15 April, 2012
• 年：2012
• 卷：159
• 期：7
• 页码：1863-1874
• 全文大小：230 K

文摘

The general condition that characterizes the possibility of action?s extension over a completion of a phase space is formulated and an example of a G-space that has no Dieudonn¨¦ complete G-extensions is given. Sufficient conditions (different kinds of rectangular conditions in products) for the action?s extensions over the Stone-?ech compactification, the Hewitt realcompactification and the Dieudonn¨¦ completion of a space are presented. Boundedness, uniform equicontinuity and quasiboundedness of actions are characterized as action?s uniform continuity on the (piecewise) semi-uniform product. From this point of view the origin of different examples of action?s extensions are explained.