Indicate whether the following the following statements are true (T) or not true
ID: 3141536 • Letter: I
Question
Indicate whether the following the following statements are true (T) or not true in general (X). No proofs or explanations are required: no partial credit is available. (a) ______ A subset of R is closed if and only if its complement is open. (b) _________ if A and B are separated sets, then no limit point of A can also be a limit point of B. (c) _______ If (x_n) is a sequence with limit x belongs to o, where o is an open set, then all but a finite number of the terms of (x_n) must be in o. (d) _____ If (x_n) is a sequence with limit x belongs to F, where F is a closed set, then all but a finite number of terms (x_n) must be in F. (e)______ If f is a function which is uniformly continuous on every interval of the form [a, b], then f is uniformly continuous on R. (f) _______ If sigma x_n and sigma y_n diverge, then sigma x_ny_n diverges also. (g) _____There exists a subset A R such that every point of A is a limit point of A. (h) __________ There exists an infinite subset A R such that no point of A is a limit point of A. (i) _____ If g is a continuous function with domain R, then the set {x|g(x) notequalto 0} is open. (j) ____ There is a rearrangement of the series sigma (-1)^n+1/n which converge to pi^e.Explanation / Answer
a.) true
b.)true
c.)false
d.)true
e.)false
f.)false
g.)true
h.)true
i.)true
j.)true