Let \(\sum (X)\) be the collection of subrings 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 \(\beta X\) 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 show 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 in Theorem 3.8.

令\（\ sum（X）\）为包含\（C ^ {*}（X）\）的C（X）子环的集合，其中X是Tychonoff空间。对于任何\（A（X）\在\总和（X）\）有与之相关联的子集\（\埃普西隆_ {A}（X）\）的\（\测试X \）其是阿的-analogue翰威特真正紧致\（\埃普西隆X \）的X。对于任何\（A（X）\ in \ sum（X）\），令[ A（X）]为所有\（B（X）\ in \ sum（X）\）的类，这样\（\ upsilon _ {A}（X）= \ upsilon _ {B}（X）\）。我们证明，对于第一个可数非紧实实压缩空间X，[ A（X）]至少包含\（2 ^ {c} \）许多不同的子代数，在定理3.8中，没有两个是同构的。