MAT237Y1 : mat2371-2openBall.pdf
Document Summary
The concept of open ball is a generalization of the interval (a , a + ), which is also denoted by. To say that xxx b( , aaa) is to say that |xxx aaa| < , or that xxx is in a delta neighborhood of the point aaa. Using this notation the continuity condition for a function f at a point aaa can be written as. Such that xxx xxx b( , aaa) = f (xxx) b( , f (aaa)) An interior point of a set s is a special point of s: it is surrounded by other interior points of s! This sounds like a puzzle: there is no interior point that is an immediate neighbor of a boundary point! This is a mystic idea and is suitable for studying the limit: remember when a variable xxx approaches a point aaa it gets closer to it but it can never reach it.
