Recently, the locally convex space theory has obtained a series of proper developments and improvements by the agency of the Basic Matrix Theorem (BMT) duc to J. Mikusinski and P. Antosik. In this note, we would like ...Recently, the locally convex space theory has obtained a series of proper developments and improvements by the agency of the Basic Matrix Theorem (BMT) duc to J. Mikusinski and P. Antosik. In this note, we would like to present another basic theorem named Uniform Convergence Principle (UCP). We shall show that UCP has the same effects as BMT, though UCP is easier than BMT in their proofs. UCP. Let G be an abelian topological group and Ωa sequentially compact space.展开更多
文摘Recently, the locally convex space theory has obtained a series of proper developments and improvements by the agency of the Basic Matrix Theorem (BMT) duc to J. Mikusinski and P. Antosik. In this note, we would like to present another basic theorem named Uniform Convergence Principle (UCP). We shall show that UCP has the same effects as BMT, though UCP is easier than BMT in their proofs. UCP. Let G be an abelian topological group and Ωa sequentially compact space.
