Let f be a real valued function defined on all reals. Prove that f is continuous if and only if for each set O of real numbers, f^-1 (O) is an open set. (You may assume that f is continuous if and only if for each closed set C of real numbers, f^-1 (C) is a closed set)
Let f be a real valued function defined on all reals. Prove that f is continuous if and only if for each set O of real numbers, f^-1 (O) is an open set. (You may assume that f is continuous if and only if for each closed set C of real numbers, f^-1 (C) is a closed set)
Chapter3: Functions
Section3.2: Domain And Range
Problem 58SE: Create a function in which the range is all nonnegative real numbers.
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Transcribed Image Text:Let f be a real valued function defined on all
reals. Prove that f is continuous if and only if
for each set O of real numbers, f^-1 (O) is an
open set. (You may assume that fis
continuous if and only if for each closed set C
of real numbers, f^-1 (C) is a closed set)
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