Abstract
The aim of this chapter is to explore the ramifications of our general metrization theory for classic functional analysis concerned with open mapping theorems, closed graph theorems, and uniform boundedness principles, for which we establish a new generation of results. Here we also prove a refinement of the classic Birkhoff–Kakutani theorem by fully bringing the topology into focus. The prevalent setting in most of the results established in this chapter is that of quasi-pseudonormed group.KeywordsUniform Boundedness Principle (UBP)General Metrization TheoryOpen Mapping Theorem (OMT)Closed Graph Theorem (CGT)Modern Functional AnalysisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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