Lattices of uniformly continuous functions

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• 作者：Fé ; lix Cabello Sá ; nchez ; ^{fcabello@unex.es} ; Javier Cabello Sá ; nchez ^coco@unex.es
• 关键词：Lattices ; Uniformly continuous functions ; Isomorphism ; Banach&ndash ; Stone theorem
• 刊名：Topology and its Applications
• 出版年：2013
• 出版时间：1 January, 2013
• 年：2013
• 卷：160
• 期：1
• 页码：50-55
• 全文大小：165 K

文摘

An explicit representation of the order isomorphisms between lattices of uniformly continuous functions on complete metric spaces is given. It is shown that every lattice isomorphism is given by the formula , where is a uniform homeomorphism and is defined by . This provides a correct proof for a statement made by Shirota sixty years ago.