MAT237Y1 : mat237 1-7.pdf
Document Summary
Recall that topology extended the idea of belonging in a more subtle way to belonging to the interior, the boundary and to the interior of the complement. To see this idea better let"s assume a point aaa 6 s. then of course the set {aaa} and the set s are disjoint in the set theoretic sense. Exercises 5 and 6 claim that in the presence of openness or closedness discontinuity and disjointness are the same. If a continuous function f is de ned on the set. S {aaa} then the values of f (aaa) must be very very close to lots of values in f (s) = {f (xxx) : xxx s}. Indeed since aaa s then there is a sequence of points from s which converge to aaa, and the image of this sequence is converging to the value f (aaa).
