We discuss some properties of linear functionals on topological hyperbolic and topological bicomplex modules. The hyperbolic and bicomplex analogues of the uniform boundedness principle, the open mapping theorem, the closed graph theorem and the Hahn Banach separation theorem are proved.

中文翻译：

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双复标量和双曲标量的泛函分析的一些基本定理

我们讨论了拓扑双曲型和拓扑双复模块上线性泛函的一些性质。证明了一致有界原理的双曲和双复类似物，开放映射定理，闭图定理和Hahn Banach分离定理。