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From: math.etsu/multicalc/Chap2/Chap2-2/index.htm

Motivation:

joelle-lancaster
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From: math.etsu/multicalc/Chap2/Chap2-2/index.htm

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  1. Motivation: To begin with, let us define any connected open set that contains a point p to be a neighborhood of p.  For example, an open ball of radius d > 0 about p, which is the set of all x such that || x-p || < d, is a neighborhood of p.  Any open rectangle containing p is also a neighborhood of p. From: http://math.etsu.edu/multicalc/Chap2/Chap2-2/index.htm

  2. Extreme Value Thm: If f: [a, b]  R is continuous, then $ c, d  [a, b] s.t. f(c) ≤ f(x) ≤ f(d) x  [a, b]. What is the minimum hypothesis such that the Extreme Value Theorem holds: Suppose f: X  Y… __________________________________________________________________ Some common symbols: • $ = there exists  = unique $ = there exists a unique •  = for all  = s.t. = such that http://www.sparknotes.com/math/calcab/applicationsofthederivative/section3.rhtml

  3. y  Y  Y : • lower case = element • Upper case = set • Caligraphy {\cal Y} = collection of sets. • _______________________________________________________________________________________________________________________ • Want to learn more about point-set topology:Do aMathSciNetsearch: http://www.ams.org/mathscinet/ Use MSC Primary: 54 for general topologyTo find other MSC numbers: http://www.ams.org/mathscinet/searchMSC.html • If you are off-campus, you will need to log into MathSciNet via the Math Library website: • http://www.lib.uiowa.edu/math/index.html • Note most articles found by MathSciNet are research articles. Unfortunately, this class will not prepare you to read most of these articles—but don’t let that stop you if you have an interest in them.

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