A Structure Theorem in Finite Topology
A Structure Theorem in Finite Topology
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有限拓扑结构定理
DOI：
10.4153/cmb-1983-019-4
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
J. Ginsburg
中科院分区：
文献类型：
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作者：
J. Ginsburg
抽象简单结构定理或表示定理在诸如代数之类的学科中出现在非常初级的水平上，但在初级拓扑学中很少遇到这样的定理。在这篇注记中，我们为有限拓扑空间提供了一个这样的定理，它只涉及最基本的概念：离散空间、非离散空间、乘积空间和同胚。我们的定理描述了那些齐次有限空间的结构。
Abstract Simple structure theorems or representation theorems make their appearance at a very elementary level in subjects such as algebra, but one infrequently encounters such theorems in elementary topology. In this note we offer one such theorem, for finite topological spaces, which involves only the most elementary concepts: discrete space, indiscrete space, product space and homeomorphism. Our theorem describes the structure of those finite spaces which are homogeneous.