Past exam of the Probability, statistics and options II course of the University of Oxford / 2007 / E / 3 / b

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- Solution b

Solution

True. A separation of

Y

into two disjoint nonempty open subsets would pull back under the continuous surjection

f

to a separation of

X

. The inverse images are nonempty by surjectivity, contradicting connectedness of

X

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

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