Finite posets and topological spaces in locally finite varieties
Finite posets and topological spaces in locally finite varieties
复制标题
局部有限簇中的有限偏序集和拓扑空间
DOI：
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发表时间：
2005
期刊：
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通讯作者：
L. Zádori
中科院分区：
文献类型：
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作者：
B. Larose;L. Zádori
摘要。我们证明了如果有限连通偏序集允许保序泰勒运算，那么它的所有同伦群都是平凡的。我们用这个给新的特征的局部有限品种省略类型1的偏序集（或等价的，有限拓扑空间）的品种。其他省略型定理的类似变种。我们给出了几个例子的偏序集，承认各种类型的泰勒运算，特别是，我们展示了一个拓扑空间，这不是一个H-空间，但兼容的一组非平凡的身份，回答问题W。Taylor.
Abstract.We prove that if a finite connected poset admits an order-preserving Taylor operation, then all of its homotopy groups are trivial. We use this to give new characterisations of locally finite varieties omitting type 1 in terms of the posets (or equivalently, finite topological spaces) in the variety. Similar variants of other omitting-type theorems are presented. We give several examples of posets that admit various types of Taylor operations; in particular, we exhibit a topological space which is not an H-space but is compatible with a set of non-trivial identities, answering a question of W. Taylor.