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An interesting example of a compact Hausdorff space that is often presented in beginning courses in topology is the unit square [0, 1]× [0, 1] with the lexicographic order topology. The closed subspac...
首先证明交换环关于I-adic拓扑诱导的完备化环是商环的有限投射极限，其次揭示Abel范畴noetherian对象与正合序列的关系，进而用范畴的方法给出希尔伯特basis定理的推论 ——noetherian环的I-adic拓扑完备化环R也是noetherian环的新证明，之后论证该推论与希尔伯特basis定理的另一推论是等价的.