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http://dx.doi.org/10.7858/eamj.2019.021

Didactical Approach on Topology -Centered on convergence and continuity-  

Kim, Jin Hwan (Department of Mathematics Education, Yeungnam University)
Publication Information
East Asian mathematical journal / v.35, no.2, 2019 , pp. 239-257 More about this Journal
Abstract
The purpose of this study is to show that the topology is closely related to some subjects learned in school mathematics and then to give motivations for learning of the topology. To do this, it is showed that the topology is an abstracted device that deal with structure of limit and continuity introduced in school mathematics. This study took a literature study. The results of this study are as follows. First, the formal definition of general topology to structure open sets was examined. The nearness relation together with the closure operation was introduced and used to characterize for construction of general topology. Second, as definitions for continuity of function, we considered the intuitive definition, definition, structured definitions using open intervals and definition using open sets and then we investigated their roles. We also examined equivalent definition using the nearness relation which is helpful to understand continuity of function. Third, the sequence and its limit are treated in terms of continuous functions having the set of natural numbers and its extended set as domains. From these, it can be concluded that the convergence of sequence and the continuity of function are identified as functions that preserve the nearness relation and that the topology is a specialized tool for dealing with convergence and continuity.
Keywords
didactical approach; topology; convergence; continuity(intuitive definition, formal definition); nearness relation;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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