M－连续格到Hilbert方体的嵌入

本文主要讨论Ｍ－连续格到Ｈｉｌｂｅｒｔ方体的嵌入问题．我们建立了Ｍ－连续格的次直积表示理论，推广并统一了Ｒａｎｅｙ，Ｂｒｕｎｓ，Ｌａｗｓｏｎ，Ｂａｎｄｅｌｔ和Ｅｒｎｅ等人的相应工作．Ｒｅｎａｙ与Ｂｒｕｎｓ的经典方法是建立在对相应的弱辅助关系的极大完备链作深入分析之上的，富于技巧性，且有局限性．与之相比，本文所使用的方体则相当朴素而自然，但却能处理更为广泛的情形．

Embeddings of M-Continuous Lattices in Hilbert Cubes

This paper is mainly devoted to the embeddings of M-continuous lattices in Hilbert cubes. we establish the subdirect product representation theory of M-continuous lattices,whichgeneralizes and unifies the corresponding work of Raneyt Bruns,Lawson,Bandelt,Erne andothers. The classical technique of Raney and Bruns,baised on the deep investigations of maximalcomplete strict chains of suitable auxiliary relations,is skillful and the situations to which it canapply are limited.comparatively,the method used in this paper not ouly is very natural andconceptual,but also can deal with more general cases.