Problem and its derivative from GR8767#64
Posted: Fri Oct 28, 2011 10:13 pm
Hi, I am going to fight MathSub in Nov. And pls help me this rub ..
64. Let S be a compact topological space, let T be a t.s., and let f be a function from S onto T. Of the following conditions on f, which is the weakest condition sufficient to ensure the compactness of T
A. f is a homeomorphism.
B. f is continuous and 1-1
C. f is continuous
D. f is 1-1
E. f is bounded.
The answer is C.
Can you explain the reason?
sfmathgre.blogspot.com only offered solutions of 05&97
And it is the derivative, tested in 2004:
f: X -> Y is continuous bijection.
I. if X is compact then Y is compact
II. if X is Hausdorff, then Y is Hausdorff
III. if X is compact and Y is Hausdorff, then f^(-1) (the inv of f) exist.
the answer provided by student of 04 is only III is right
Why the first statement is wrong?
64. Let S be a compact topological space, let T be a t.s., and let f be a function from S onto T. Of the following conditions on f, which is the weakest condition sufficient to ensure the compactness of T
A. f is a homeomorphism.
B. f is continuous and 1-1
C. f is continuous
D. f is 1-1
E. f is bounded.
The answer is C.
Can you explain the reason?
sfmathgre.blogspot.com only offered solutions of 05&97
And it is the derivative, tested in 2004:
f: X -> Y is continuous bijection.
I. if X is compact then Y is compact
II. if X is Hausdorff, then Y is Hausdorff
III. if X is compact and Y is Hausdorff, then f^(-1) (the inv of f) exist.
the answer provided by student of 04 is only III is right
Why the first statement is wrong?