标题： 完全不连通（非度量）Gelfand对偶性 显示英文标题

标题： Totally Disconnected (non-metric) Gelfand Duality

摘要： 我们表征那些在不连通的均匀完备拓扑域上的代数，这些代数可以表示为紧致拓扑空间上的连续函数代数，从而推广了非阿基米德赋范域的Gelfand对偶性（Van der Put定理）。 更一般地，我们为任何拓扑域F建立了紧致F-Tychonoff空间范畴与一个自然的交换F-代数范畴之间的（对偶）伴随关系，对于满足Stone-Weierstrass定理的域，这种伴随关系成为对偶性。 为了获得这些结果，我们没有利用分析工具，而是使用了域的规范群均匀性和代数的内在性质。 显示英文摘要

摘要： We characterize those algebras over a disconnected uniformly complete topological field which are represenable as algebras of continuous functions on compact topologicla spaces, generalizing thus Gelfand duality for non-archimedean normed fields (Van der Put theorem). More generally, we establish for any topological field F a (dual) adjunction between the category of compact F-Tychonoff spaces and a natural category of commutative F-algebras, which becomes a duality for fields satisfying the Stone-Weierstrass theorem. To obtain these results we do not utilize analytic tools, but the canonical group uniformity of the field and intrinsic properties of the algebras.