2017/01/19 by Fouad Naderi, Naderi, Fouad
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #Numerical Methods and Algorithms
paper · pdf · doi:10.48550/arxiv.1701.05668
openalex publication_date 2017/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We learn mathematics subjectively and must apply it objectively. But\nsometimes, we apply it subjectively by using wrong intuitions which may be\nelusive to our eyes. The aim of this note is to disclose the secretes of two\nkinds of these false intuitions and the opportunities they may provide. We\nfirst discuss the wrong assumption which says that each topology is uniquely\ndetermined by studying a very bad phenomenon happening in dealing with weak*\ntopology. Then, we consider the problem of completing a normed space under two\ncomparable norms, one being smaller than the other. Here, we show that the\ncommon belief contending that smaller norms give rise to larger completions is\nwrong. We then pose some serious questions arising from these wrong intuitions.\nAs we will see finding fallacies are as important as major mathematical\nactivities like proving and disproving.\n