A TOPOLOGICAL CHARACTERIZATION OF GLEASON PARTS
A TOPOLOGICAL CHARACTERIZATION OF GLEASON PARTS
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格里森零件的拓扑特性
DOI：
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发表时间：
1967
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通讯作者：
J. Garnett
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作者：
J. Garnett
假设X是紧Hausdorff空间，a是C(X)的一个子代数，9是X上连续复值函数的代数，假设a分隔X上的点，包含常数函数，并且是一致闭的。在弱星型拓扑下，A的极大理想空间M(A)是紧化的Hausdorff空间。我们认为X嵌入在M(A)中，而A是M(A)上的函数代数。Gleason在[4]中指出，当泛函范数|| x - y \Λ* < 2时，可以通过设x ~ y在M(A)上定义等价关系。这种关系的等价类称为M(A)的“部分”。在某些情况下，部分被用来对M(A)施加解析结构（例如[7]）β设P是某个M(A)的一部分。那么很明显P是一个完全规则的空间并且我们有固定的P
Suppose X is a compact Hausdorff space and A is a subalgebra of C(X)9 the algebra of continuous complex valued functions on X. Assume A separates the points of X, contains the constant functions, and is uniformly closed. A is then called a function algebra on X. With the weak star topology, the maximal ideal space M(A) of A is a compact Hausdorff space. We consider X as embedded in M(A) and A as a function algebra on M(A). In [4] Gleason noted that an equivalence relation could be defined on M(A) by setting x ~ y when the functional norm || x — y \Λ* < 2. The equivalence classes for this relation are called the "parts" of M(A). In certain cases parts have been used to impose an analytic structure on M(A) (see for example [7])β Let P be a part of some M(A). Then clearly P is a completely regular space and fixing p e P we have