A sharp representation of multiplicative isomorphisms of uniformly continuous functions

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• 作者：Javier Cabello Sá ; nchez ^{coco@unex.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：46E25 ; 54C35
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：197
• 期：Complete
• 页码：1-9
• 全文大小：291 K

文摘

Let X, Y   be complete metric spaces, U(X)$U(X)$, U(Y)$U(Y)$ the spaces of uniformly continuous functions with real values defined on X and Y  . We will show the form that every multiplicative isomorphism T:U(Y)→U(X)$T:U(Y)\to U(X)$ has: for x   outside a uniformly isolated subset S⊂X$S\subset X$, where 46767b681bff30" title="Click to view the MathML source">τ:X→Y$\tau :X\to Y$ is a uniform homeomorphism and p:X∖S→R$p:X\setminus S\to \mathbb{R}$ is such that p⋅h⋅log⁡h$p\cdot h\cdot \log h$ is uniformly continuous for every h∈U(X,(2,∞))$h\in U(X,(2,\infty ))$.