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lmtuan · 2005 March 3rd, 06:55 AM

According to Dragonfinity:
* S is a connected subset of R.
* S is not necessary open.
( I agree with Dragonfinity).
Since f is a real-valued function defined and continuous on the set of real numbers R, f is continuous on [0,1]. Thus, f([0.1]) is bounded. In other hand, we have S is a subset of f([0,1]). Hence, S is a bounded subset of R.
Answer: (C)

2005 March 3rd, 06:55 AM	#4 (permalink)
lmtuan Within my grasp! Join Date: Oct 2004 Location: Vietnam Posts: 107	Re: Open vs. connected subsets According to Dragonfinity: * S is a connected subset of R. * S is not necessary open. ( I agree with Dragonfinity). Since f is a real-valued function defined and continuous on the set of real numbers R, f is continuous on [0,1]. Thus, f([0.1]) is bounded. In other hand, we have S is a subset of f([0,1]). Hence, S is a bounded subset of R. Answer: (C) _ _ _ _ SIG _ _ _ _ lmtuan --------------------