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?