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On The Equivalence Of The Ring, Lattice, And Semigroup Of Continuous Functions, Melvin Henriksen
On The Equivalence Of The Ring, Lattice, And Semigroup Of Continuous Functions, Melvin Henriksen
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A large number of papers have been published that are devoted to showing that certain algebraic objects obtained by defining operations on the set of all continuous real-valued functions on a suitably restricted topological space determine the space. We mention but a few of them in this article.
On Rings Of Bounded Continuous Functions With Values In A Division Ring, Ellen Correl, Melvin Henriksen
On Rings Of Bounded Continuous Functions With Values In A Division Ring, Ellen Correl, Melvin Henriksen
All HMC Faculty Publications and Research
Let C*(X, A) denote the ring of bounded continuous functions on a (Hausdorff) topological space X with values in a topological division ring A. If, for every maximal (two-sided) ideal M of C*(X, A), we have C*(X, A)/M is isomorphic with A, we say that Stone's theorem holds for C*(X, A). It is well known [9; 6] that Stone's theorem holds for C*(X, A) if A is locally compact and connected, or a finite field. In giving a partial answer to a question of Kaplansky [7], Goldhaber and Wolk showed in [5] that, with restriction on X, and if A …