Abstract

For a given group \((G,X,\alpha)\) of topological transformations on a Tikhonov space \(X\), a group \((I(G, X), I(X), I(\alpha))\) of topological transformations on the space \(I(X)\) of idempotent probability measures is constructed. It is shown that, if the action \(\alpha\) of the group \(G\) is open, then the action \(I(\alpha)\) of the group \(I(G,X)\) is also open; while an example is given showing that the openness of the action \(\alpha\) is substantial. It has been established that, if the diagonal product \(\Delta f_{p}\) of a given family \(\{f_{p}, f_{pq}; A\}\) of continuous mappings is an embedding, then the diagonal product \(\Delta I(f_{p})\) of the family \(\{I(f_{p}), I(f_{pq}); A\}\) of continuous mappings is also an embedding. A Dugundji compactness criterion for the space of idempotent probability measures is obtained.

中文翻译：

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Dugundji Compacta 和幂等概率测度空间

摘要

对于给定的吉洪诺夫空间\(X\)上的拓扑变换群\((G,X,\alpha)\)，群\((I(G, X), I(X), I(\alpha)构造幂等概率测度空间\(I(X)\)上的拓扑变换))\) 。表明，如果群\(G\)的动作\(\alpha\)是开的，则群\(I(G,X)\)的动作\(I(\alpha)\)也开放；同时给出的例子表明，动作\(\alpha\)的开放性是巨大的。已经确定，如果连续映射的给定族\(\{f_{p}, f_{pq}; A\}\)的对角积\(\Delta f_ {p}\)是一个嵌入，那么连续映射族\(\{I(f_{p}), I(f_{pq}); A\}\) 的对角积\(\Delta I( f_{p})\)也是一个嵌入。获得幂等概率测度空间的 Dugundji 紧致准则。