AN HISTORICAL-EPISTEMOLOGICAL ANALYSIS OF CONTINUITY IN METRIC AND TOPOLOGICAL SPACES
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Abstract
The concept of continuous mapping in , metric and topological spaces is one of the central concepts of analysis and an important concept of topology. This paper presents a historical epistemological analysis that clarifies the genesis and development of the concept of continuous mapping in the real number set , the metric spaces, and the topological spaces throughout the periods from prehistoric to modern. The results of the historical epistemological analysis can help teacher educators visualize the obstacles that mathematics students face when learning this knowledge so that they can design their lessons in a more reasonable way.
Keywords
continuous function, continuous mapping, epistemological analysis, metric space, topological space
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References
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