论文标题
关于C（x）的非同构中间环的基数
On Cardinality Of Non Isomorphic Intermediate Rings Of C(X)
论文作者
论文摘要
令$ \ sum（x）$是包含$ c^{*}（x）$的$ c（x）$的子algebras的集合，其中$ x $是tychonoff空间。对于任何$ a（x）\ in \ sum（x）$，都有关联的子集$ \ upsilon_ {a}（x）$ $βX$，这是$ a $ a $ a-a $ a-analogue the hewitt real compactification $ \ upsilon x $ x $的$ \ upsilon x $。对于任何$ a（x）\ in \ sum（x）$，令$ [a（x）] $为所有$ b（x）\ in \ sum（x）$的类别，这样$ \ upsilon_ {a}（x）= \ upsilon_ = \ upsilon_ {b}（x）$。我们已经证明，对于第一个可计数的非紧凑型真实紧凑空间$ x $，$ [a（x）] $至少包含$ 2^{c} $许多不同的subergebras，其中两个是同构的。
Let $\sum (X)$ be the collection of subalgebras of $C(X)$ containing $C^{*}(X)$, where $X$ is a Tychonoff space. For any $A(X)\in \sum(X)$ there is associated a subset $\upsilon_{A}(X)$ of $βX$ which is an $A$-analogue of the Hewitt real compactification $\upsilon X$ of $X$. For any $A(X)\in \sum(X)$, let $[A(X)]$ be the class of all $B(X)\in \sum(X)$ such that $\upsilon_{A}(X)=\upsilon_{B}(X)$. We have shown that for first countable non compact real compact space $X$, $[A(X)]$ contains at least $2^{c}$ many different subalgebras no two of which are isomorphic.
