# Continuous image of a Paracompact space need not be Paracompact.

The following is an exercise in Topology by Munkres.

• Show that if f is a continuous map from X to Y where X is paracompact then the subspace f(X) of Y need not be paracompact.

I am having trouble constructing such a function. Any help would be appreciated. Thank You.

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HINT: Every discrete space is paracompact, and every map whose domain is a discrete space is continuous. Find a non-paracompact space $Y$ and just ...

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Oh!Thank You. I feel stupid now. –  user20694 Apr 9 '12 at 2:20
@user20694: We’ve all been there a time or two. :-) –  Brian M. Scott Apr 9 '12 at 2:22