THE INTERIOR, CLOSURE and BOUNDARY OF A SET (cont'd) - Lec 10 - Mathematics for Economists I

THE INTERIOR, CLOSURE and BOUNDARY OF A SET (cont'd) - Lec 10 - Mathematics for Economists I

Topology closure Metric Space
Free
47 minutes
English

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The content begins by exploring isolated points within a set and determining that none exist in this context. However, it then discusses how certain points can be considered isolated based on their distance from other points within the set. The importance of understanding the number of points (denoted as 'n') is also highlighted, particularly when dealing with sets of two or more elements. Furthermore, the concept of limit points is introduced, which are essentially cluster points in this context. A specific example of a set in R2 is provided to illustrate these concepts. The definition of boundary points is then explained, focusing on their relation to an epsilon ball and how they satisfy certain conditions. Additionally, the content examines isolated points within R2 as boundary points, taking into account the properties of an epsilon ball surrounding such points. learn more

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