22M:132: Topology Exam 1
Sept 30, 2008
[10] 1.) Definition: The point x∈Xis a limit point of Aif
[12] 2.) Suppose R= the set of real numbers has the standard topology. Let Q= the set of
rational numbers. Calculate the following in R:
Qo=Q=Q0=
3.) The following two statements are false. Show that the statements are false by providing counter-
examples. You do not need to explain your counter-examples.
[9] 3a.) If xn∈A, then there exists a unique point x∈Asuch that xn→x.
[9] 3b.) If f:X→Yis continuous, then f(A)⊂f(A).
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