MAT237Y1 Study Guide - Closed Set, Open Set

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A function f : a rm (where a is a subset of rn) is said to be continuous at a point a point aaa a if. Such that x s |xxx aaa| < = |f (xxx) f (aaa)| < . It is like a game that two players play. We will soon see what this relationship means. The set s in 1. 13 is known as the inverse image of the set u under f . We shall study this concept later, but for now just take it as a piece of language; a convention. For example f (rm) = a and f ( ) = (why?) Now using this notation we can see that the de nition of continuity translates to: Such that x a xxx b( , aaa) = xxx f (b( , f (aaa))) which can further translate to. Such that b( , aaa) f (b( , f (aaa)))

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