Past exam of the options II course of the University of Oxford / 2007 / E / E3 / a

Table of contents
- Solution a

Solution

True. Pull an open cover of

Y

back through

f

. Surjectivity makes those inverse images cover

X

. A finite subcover of the compact space

X

maps back to a finite subcover of

Y

. Thus a continuous image of a compact space is compact.

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