English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We learn mathematics subjectively and must apply it objectively. Butsometimes, we apply it subjectively by using wrong intuitions which may beelusive to our eyes. The aim of this note is to disclose the secretes of twokinds of these false intuitions and the opportunities they may provide. Wefirst discuss the wrong assumption which says that each topology is uniquelydetermined by studying a very bad phenomenon happening in dealing with weak*topology. Then, we consider the problem of completing a normed space under twocomparable norms, one being smaller than the other. Here, we show that thecommon belief contending that smaller norms give rise to larger completions iswrong. We then pose some serious questions arising from these wrong intuitions.As we will see finding fallacies are as important as major mathematicalactivities like proving and disproving.

How wrong intuitions about weak* topology and completions of a normed space pose serious problems